This section discusses using special product patterns to multiply polynomials, providing 4 examples of multiplying polynomials using these patterns. It encourages learning science and math together and is from page 572 with problems 3-39 through 40.
This section discusses applying exponent properties involving products. It provides 5 examples of using exponent properties when multiplying terms with the same base. Each example solves a short problem using exponent properties and rules for multiplying terms with the same base.
This document provides an overview of polynomials including:
- Defining polynomials and their key terms like degree and leading coefficient
- Combining like terms through addition and subtraction of polynomials
- Multiplying polynomials by distributing one polynomial across each term of the other
- Special products like difference of squares and perfect square binomials that have recognizable patterns
This document discusses polynomial functions. A polynomial is a sum of monomials, and a polynomial function with a single variable is called a polynomial function. The degree of a polynomial is the highest exponent of its variable, and the leading coefficient is the coefficient of the term with the highest degree. Polynomial functions are classified based on their degree as linear, quadratic, cubic, etc. The document also discusses evaluating polynomial functions for different inputs, the general shapes of polynomial functions based on degree and leading coefficient, and the remainder and factor theorems.
Polynomial functions are functions with exponents that are positive whole numbers. They can be expressed in standard or factored form and have different degrees corresponding to the highest power of x. Second-degree polynomials have the highest power of x being squared, like x^2 + 2x + 5. Their zeros and x-intercepts are opposites, except when there is a zero of multiplicity 2. Third-degree polynomials have the highest power being cubed, like x^3 + x - 3. Fourth-degree polynomials have the highest power being the fourth power, like x^4 - x^2 + 1.
This document discusses the use of theory in quantitative, qualitative, and mixed methods research. It provides definitions of theory for quantitative research as sets of interrelated variables and hypotheses about relationships between variables. Qualitative research may use theoretical lenses to guide examination of important issues and populations. Theories in qualitative research can emerge inductively from themes in the data. Mixed methods research can incorporate deductive testing and inductive emerging theories, and theories can act as lenses to guide studies.
This document introduces special products and factors of polynomials. It discusses how patterns can be used to simplify algebraic expressions and solve geometric problems. Students will learn to identify special products through pattern recognition, find special products of polynomials, and apply these concepts to real-world problems. The goals are to demonstrate understanding of key concepts and solve practice problems accurately using different strategies.
The lymphatic system helps destroy microorganisms, absorbs tissue fluid and transports it back to the bloodstream, and helps fight illnesses and infections. It is composed of lymph vessels, lymph nodes, lymphocytes like B and T cells, the spleen, thymus gland, tonsils, and bone marrow. Together these parts work to filter lymph, produce white blood cells, and defend the body against pathogens.
Blood transports oxygen, nutrients, hormones, carbon dioxide, and waste throughout the body. It also fights infections through white blood cells and helps regulate temperature. Blood is made up of plasma, platelets, red blood cells, and white blood cells. It exists in different blood types (A, B, AB, O) and Rh factors (+ or -) to prevent incompatible mixing. Diseases can affect blood cells like leukemia and anemia.
This section discusses applying exponent properties involving products. It provides 5 examples of using exponent properties when multiplying terms with the same base. Each example solves a short problem using exponent properties and rules for multiplying terms with the same base.
This document provides an overview of polynomials including:
- Defining polynomials and their key terms like degree and leading coefficient
- Combining like terms through addition and subtraction of polynomials
- Multiplying polynomials by distributing one polynomial across each term of the other
- Special products like difference of squares and perfect square binomials that have recognizable patterns
This document discusses polynomial functions. A polynomial is a sum of monomials, and a polynomial function with a single variable is called a polynomial function. The degree of a polynomial is the highest exponent of its variable, and the leading coefficient is the coefficient of the term with the highest degree. Polynomial functions are classified based on their degree as linear, quadratic, cubic, etc. The document also discusses evaluating polynomial functions for different inputs, the general shapes of polynomial functions based on degree and leading coefficient, and the remainder and factor theorems.
Polynomial functions are functions with exponents that are positive whole numbers. They can be expressed in standard or factored form and have different degrees corresponding to the highest power of x. Second-degree polynomials have the highest power of x being squared, like x^2 + 2x + 5. Their zeros and x-intercepts are opposites, except when there is a zero of multiplicity 2. Third-degree polynomials have the highest power being cubed, like x^3 + x - 3. Fourth-degree polynomials have the highest power being the fourth power, like x^4 - x^2 + 1.
This document discusses the use of theory in quantitative, qualitative, and mixed methods research. It provides definitions of theory for quantitative research as sets of interrelated variables and hypotheses about relationships between variables. Qualitative research may use theoretical lenses to guide examination of important issues and populations. Theories in qualitative research can emerge inductively from themes in the data. Mixed methods research can incorporate deductive testing and inductive emerging theories, and theories can act as lenses to guide studies.
This document introduces special products and factors of polynomials. It discusses how patterns can be used to simplify algebraic expressions and solve geometric problems. Students will learn to identify special products through pattern recognition, find special products of polynomials, and apply these concepts to real-world problems. The goals are to demonstrate understanding of key concepts and solve practice problems accurately using different strategies.
The lymphatic system helps destroy microorganisms, absorbs tissue fluid and transports it back to the bloodstream, and helps fight illnesses and infections. It is composed of lymph vessels, lymph nodes, lymphocytes like B and T cells, the spleen, thymus gland, tonsils, and bone marrow. Together these parts work to filter lymph, produce white blood cells, and defend the body against pathogens.
Blood transports oxygen, nutrients, hormones, carbon dioxide, and waste throughout the body. It also fights infections through white blood cells and helps regulate temperature. Blood is made up of plasma, platelets, red blood cells, and white blood cells. It exists in different blood types (A, B, AB, O) and Rh factors (+ or -) to prevent incompatible mixing. Diseases can affect blood cells like leukemia and anemia.
The circulatory system transports blood throughout the body via blood vessels. The heart pumps blood through two circuits - systemic circulation carries blood to the body and pulmonary circulation carries blood to and from the lungs. Blood flows from the heart through arteries, then narrows into smaller arterioles and capillaries where nutrients and gases are exchanged with body tissues before returning to the heart through veins. Maintaining healthy blood pressure can prevent circulatory diseases like heart attacks and strokes.
The respiratory system takes in oxygen and removes carbon dioxide through breathing. Breathing is controlled by the diaphragm muscle contracting and relaxing. Air enters the nose and is warmed and filtered before reaching the lungs. In the lungs, bronchioles branch into alveoli where gas exchange occurs and oxygen enters the blood while carbon dioxide leaves. The respiratory and circulatory systems work together to maintain homeostasis in the body.
The excretory system collects and eliminates waste from the body through various organs including the kidneys, ureters, bladder and urethra. The kidneys filter waste from the blood to produce urine, which is stored in the bladder and then passed out of the body through the urethra. The excretory system works to maintain homeostasis by regulating fluid levels and removing toxins.
The digestive system breaks down food into small molecules that can be absorbed and used by the body. Food goes through four steps - ingestion, digestion, absorption, and elimination. Digestion involves both mechanical and chemical breakdown of food. Enzymes produced throughout the digestive system aid in chemical digestion. The major organs of the digestive system include the mouth, esophagus, stomach, small intestine, large intestine, liver, pancreas, and gallbladder.
The skin is the largest organ of the body and acts as a protective barrier. It has three layers - the epidermis, dermis and fatty layer. The skin protects the body from damage, regulates temperature and moisture, produces vitamin D, and detects sensations like touch, temperature and pain. When injured, the skin repairs through processes like scabbing, bruising and wound healing. The skin works to maintain homeostasis by regulating the internal environment and working with other body systems.
The muscular system consists of three types of muscles - skeletal, smooth, and cardiac. Skeletal muscles are voluntary and attach to bones to enable movement. Smooth muscles line organs and blood vessels to regulate movement within the body. Cardiac muscle is only found in the heart to pump blood throughout the body. Muscles contract and relax to perform functions like movement, stability, protection, and temperature regulation. A healthy diet and exercise are important to maintain strong, healthy muscles. The muscular system also helps maintain homeostasis by regulating temperature and transporting oxygen and waste throughout the body.
Charles Darwin developed the theory of evolution by natural selection after observing variations in species on the Galapagos Islands. He noticed that tortoises, finches, and other animals had adapted to their environments over time through traits that improved their chances of survival, such as tortoises developing different neck lengths corresponding to the plants available on each island. Darwin's theory explained how evolution can occur gradually through natural selection acting upon heritable variations that increase organisms' likelihood of surviving and reproducing.
DNA contains genes that provide instructions for making proteins. DNA has a double helix structure with two strands coiled around each other. Each strand contains repeating sequences of nucleotides with one of four nitrogen bases (A, T, C, G). RNA is similar but single-stranded and helps carry instructions from DNA in the nucleus to the cell's protein-making machinery. Mutations can occur during DNA replication, resulting in changes to genes that may cause genetic disorders or beneficial trait variations.
The document discusses the concepts of inheritance, genes, alleles, genotypes, phenotypes, and patterns of inheritance. It explains that chromosomes contain genes which control traits, and that offspring inherit genes from both parents. Genotypes are an organism's combination of alleles, while phenotypes are the observable traits. Dominant and recessive alleles can interact in different inheritance patterns like incomplete dominance, codominance, multiple alleles, and polygenic inheritance. An organism's environment and multiple genes can also influence phenotypes. Some disorders are caused by recessive or sex-linked genes.
Gregor Mendel performed experiments with pea plants from 1856 to 1863 to study heredity. He found that pea plants have traits such as flower color and seed shape that are inherited. Through controlled breeding experiments involving over 28,000 pea plants, Mendel discovered that traits are passed to offspring through discrete factors, now known as genes, and that some traits are dominant over recessive traits. His findings disproved the prevailing theory of blending inheritance and established the basic principles of genetics.
Asexual reproduction allows organisms to reproduce without meiosis and fertilization, resulting in offspring that are genetically identical to the parent. It occurs through various methods like fission, budding, regeneration, vegetative reproduction, and cloning. Fission involves a prokaryotic cell splitting into two identical daughter cells. Budding occurs when an outgrowth from the parent develops into a new individual. Regeneration involves regrowing a new individual from a fragment of the parent. Vegetative reproduction is seen in plants that produce new individuals from stems, leaves, or other vegetative plant structures. Cloning produces genetically identical copies in a laboratory setting. Asexual reproduction allows for rapid population growth without locating a mate. [/SUMMARY]
Sexual reproduction involves the combination of genetic material from two parent cells to form a new cell. It occurs through meiosis which produces haploid sex cells with half the number of chromosomes and through fertilization where an egg and sperm join. This maintains the diploid number of chromosomes and generates genetic variation in offspring, providing advantages for adaptation and selective breeding.
This document discusses the levels of organization of living things from atoms to organisms. It begins by explaining that all matter is made of atoms which combine to form molecules and cells. Cells make up unicellular and multicellular organisms. Unicellular organisms consist of a single cell and can be prokaryotic or eukaryotic. Multicellular organisms are made of many eukaryotic cells that differentiate and organize into tissues and organs to carry out specific functions needed for organism survival.
The cell cycle consists of interphase and the mitotic phase. Interphase includes three stages (G1, S, G2) where the cell grows and duplicates its DNA. The mitotic phase includes mitosis, where the cell nucleus and chromosomes divide, and cytokinesis, where the cell cytoplasm divides to form two daughter cells each with the same genetic material as the original cell. Cell division through the cell cycle enables growth, development, replacement of old/damaged cells, and repair of injuries in multicellular organisms.
Cellular respiration is a series of chemical reactions that convert energy from food into a usable form called ATP. It takes place in two steps - glycolysis in the cytoplasm breaks down glucose, producing some ATP and precursor molecules, while the second step in mitochondria uses oxygen to break down these precursors and produce much more ATP. Fermentation is an alternative pathway used without oxygen to produce less ATP. Photosynthesis converts light energy, carbon dioxide, and water into glucose and oxygen through reactions in chloroplasts.
The document discusses different types of transport across cell membranes. It explains that cell membranes are semipermeable and allow certain materials to pass through. Small molecules can pass through passively via diffusion, osmosis, or facilitated diffusion without using energy. Larger molecules and substances moving against a concentration gradient require active transport which uses the cell's energy. Other processes like endocytosis and exocytosis allow larger particles and molecules to enter or exit cells.
Cells come in a wide range of sizes, with human egg cells being the largest at around 1/10 the size of a period at the end of a sentence in 12 point font. Bacteria are much smaller, with around 8,000 bacteria able to fit inside a single human egg cell. All cells share some common traits, including a cell membrane that regulates interactions between the cell and its environment, cytoplasm located inside the cell, and hereditary material called DNA that controls the cell. However, plant, bacteria, and other cell types can also contain additional structures like a cell wall, chloroplasts, or flagella.
English scientist Robert Hooke first observed cells in cork over 300 years ago under a microscope. Scientists later established that all living things are composed of cells, the smallest unit of life, and that new cells arise only from pre-existing cells, according to the cell theory. Cells contain water and four basic macromolecules - nucleic acids which carry genetic information, proteins which perform most cell functions, lipids which form cell membranes and store energy, and carbohydrates which store energy and provide structure.
Acids and bases are defined by whether they produce hydronium (H3O+) or hydroxide (OH-) ions when dissolved in water. Acids have a pH below 7 and produce more H3O+ ions, bases have a pH above 7 and produce more OH- ions, and neutral solutions have an equal concentration of both ions and a pH of 7. The pH scale quantifies exactly how acidic or basic a solution is, with each unit of pH representing a tenfold change in hydronium ion concentration. pH can be measured approximately with indicators or more precisely with a pH meter. Common acids and bases have various uses from food preparation to cleaning products.
The circulatory system transports blood throughout the body via blood vessels. The heart pumps blood through two circuits - systemic circulation carries blood to the body and pulmonary circulation carries blood to and from the lungs. Blood flows from the heart through arteries, then narrows into smaller arterioles and capillaries where nutrients and gases are exchanged with body tissues before returning to the heart through veins. Maintaining healthy blood pressure can prevent circulatory diseases like heart attacks and strokes.
The respiratory system takes in oxygen and removes carbon dioxide through breathing. Breathing is controlled by the diaphragm muscle contracting and relaxing. Air enters the nose and is warmed and filtered before reaching the lungs. In the lungs, bronchioles branch into alveoli where gas exchange occurs and oxygen enters the blood while carbon dioxide leaves. The respiratory and circulatory systems work together to maintain homeostasis in the body.
The excretory system collects and eliminates waste from the body through various organs including the kidneys, ureters, bladder and urethra. The kidneys filter waste from the blood to produce urine, which is stored in the bladder and then passed out of the body through the urethra. The excretory system works to maintain homeostasis by regulating fluid levels and removing toxins.
The digestive system breaks down food into small molecules that can be absorbed and used by the body. Food goes through four steps - ingestion, digestion, absorption, and elimination. Digestion involves both mechanical and chemical breakdown of food. Enzymes produced throughout the digestive system aid in chemical digestion. The major organs of the digestive system include the mouth, esophagus, stomach, small intestine, large intestine, liver, pancreas, and gallbladder.
The skin is the largest organ of the body and acts as a protective barrier. It has three layers - the epidermis, dermis and fatty layer. The skin protects the body from damage, regulates temperature and moisture, produces vitamin D, and detects sensations like touch, temperature and pain. When injured, the skin repairs through processes like scabbing, bruising and wound healing. The skin works to maintain homeostasis by regulating the internal environment and working with other body systems.
The muscular system consists of three types of muscles - skeletal, smooth, and cardiac. Skeletal muscles are voluntary and attach to bones to enable movement. Smooth muscles line organs and blood vessels to regulate movement within the body. Cardiac muscle is only found in the heart to pump blood throughout the body. Muscles contract and relax to perform functions like movement, stability, protection, and temperature regulation. A healthy diet and exercise are important to maintain strong, healthy muscles. The muscular system also helps maintain homeostasis by regulating temperature and transporting oxygen and waste throughout the body.
Charles Darwin developed the theory of evolution by natural selection after observing variations in species on the Galapagos Islands. He noticed that tortoises, finches, and other animals had adapted to their environments over time through traits that improved their chances of survival, such as tortoises developing different neck lengths corresponding to the plants available on each island. Darwin's theory explained how evolution can occur gradually through natural selection acting upon heritable variations that increase organisms' likelihood of surviving and reproducing.
DNA contains genes that provide instructions for making proteins. DNA has a double helix structure with two strands coiled around each other. Each strand contains repeating sequences of nucleotides with one of four nitrogen bases (A, T, C, G). RNA is similar but single-stranded and helps carry instructions from DNA in the nucleus to the cell's protein-making machinery. Mutations can occur during DNA replication, resulting in changes to genes that may cause genetic disorders or beneficial trait variations.
The document discusses the concepts of inheritance, genes, alleles, genotypes, phenotypes, and patterns of inheritance. It explains that chromosomes contain genes which control traits, and that offspring inherit genes from both parents. Genotypes are an organism's combination of alleles, while phenotypes are the observable traits. Dominant and recessive alleles can interact in different inheritance patterns like incomplete dominance, codominance, multiple alleles, and polygenic inheritance. An organism's environment and multiple genes can also influence phenotypes. Some disorders are caused by recessive or sex-linked genes.
Gregor Mendel performed experiments with pea plants from 1856 to 1863 to study heredity. He found that pea plants have traits such as flower color and seed shape that are inherited. Through controlled breeding experiments involving over 28,000 pea plants, Mendel discovered that traits are passed to offspring through discrete factors, now known as genes, and that some traits are dominant over recessive traits. His findings disproved the prevailing theory of blending inheritance and established the basic principles of genetics.
Asexual reproduction allows organisms to reproduce without meiosis and fertilization, resulting in offspring that are genetically identical to the parent. It occurs through various methods like fission, budding, regeneration, vegetative reproduction, and cloning. Fission involves a prokaryotic cell splitting into two identical daughter cells. Budding occurs when an outgrowth from the parent develops into a new individual. Regeneration involves regrowing a new individual from a fragment of the parent. Vegetative reproduction is seen in plants that produce new individuals from stems, leaves, or other vegetative plant structures. Cloning produces genetically identical copies in a laboratory setting. Asexual reproduction allows for rapid population growth without locating a mate. [/SUMMARY]
Sexual reproduction involves the combination of genetic material from two parent cells to form a new cell. It occurs through meiosis which produces haploid sex cells with half the number of chromosomes and through fertilization where an egg and sperm join. This maintains the diploid number of chromosomes and generates genetic variation in offspring, providing advantages for adaptation and selective breeding.
This document discusses the levels of organization of living things from atoms to organisms. It begins by explaining that all matter is made of atoms which combine to form molecules and cells. Cells make up unicellular and multicellular organisms. Unicellular organisms consist of a single cell and can be prokaryotic or eukaryotic. Multicellular organisms are made of many eukaryotic cells that differentiate and organize into tissues and organs to carry out specific functions needed for organism survival.
The cell cycle consists of interphase and the mitotic phase. Interphase includes three stages (G1, S, G2) where the cell grows and duplicates its DNA. The mitotic phase includes mitosis, where the cell nucleus and chromosomes divide, and cytokinesis, where the cell cytoplasm divides to form two daughter cells each with the same genetic material as the original cell. Cell division through the cell cycle enables growth, development, replacement of old/damaged cells, and repair of injuries in multicellular organisms.
Cellular respiration is a series of chemical reactions that convert energy from food into a usable form called ATP. It takes place in two steps - glycolysis in the cytoplasm breaks down glucose, producing some ATP and precursor molecules, while the second step in mitochondria uses oxygen to break down these precursors and produce much more ATP. Fermentation is an alternative pathway used without oxygen to produce less ATP. Photosynthesis converts light energy, carbon dioxide, and water into glucose and oxygen through reactions in chloroplasts.
The document discusses different types of transport across cell membranes. It explains that cell membranes are semipermeable and allow certain materials to pass through. Small molecules can pass through passively via diffusion, osmosis, or facilitated diffusion without using energy. Larger molecules and substances moving against a concentration gradient require active transport which uses the cell's energy. Other processes like endocytosis and exocytosis allow larger particles and molecules to enter or exit cells.
Cells come in a wide range of sizes, with human egg cells being the largest at around 1/10 the size of a period at the end of a sentence in 12 point font. Bacteria are much smaller, with around 8,000 bacteria able to fit inside a single human egg cell. All cells share some common traits, including a cell membrane that regulates interactions between the cell and its environment, cytoplasm located inside the cell, and hereditary material called DNA that controls the cell. However, plant, bacteria, and other cell types can also contain additional structures like a cell wall, chloroplasts, or flagella.
English scientist Robert Hooke first observed cells in cork over 300 years ago under a microscope. Scientists later established that all living things are composed of cells, the smallest unit of life, and that new cells arise only from pre-existing cells, according to the cell theory. Cells contain water and four basic macromolecules - nucleic acids which carry genetic information, proteins which perform most cell functions, lipids which form cell membranes and store energy, and carbohydrates which store energy and provide structure.
Acids and bases are defined by whether they produce hydronium (H3O+) or hydroxide (OH-) ions when dissolved in water. Acids have a pH below 7 and produce more H3O+ ions, bases have a pH above 7 and produce more OH- ions, and neutral solutions have an equal concentration of both ions and a pH of 7. The pH scale quantifies exactly how acidic or basic a solution is, with each unit of pH representing a tenfold change in hydronium ion concentration. pH can be measured approximately with indicators or more precisely with a pH meter. Common acids and bases have various uses from food preparation to cleaning products.