Special factor patterns
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The document provides examples and rules for factoring different types of expressions: 1) It shows how to factor expressions of the form a^2 - b^2 into (a+b)(a-b) and gives an example. 2) It explains how to factor square trinomials of the form x^2 + bx + c by finding two factors of c that sum to b. 3) It discusses factoring expressions involving squares and how exponents work.
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The document provides examples and explanations of adding, subtracting, multiplying, and expanding polynomials. It demonstrates multiplying polynomials using the FOIL (First, Outer, Inner, Last) method and provides examples of sum and difference of squares, square of a binomial, cube of a binomial, and multiplying three binomials. Common patterns that arise when multiplying polynomials are identified.
Class 9
This document contains 54 multiple choice questions related to polynomials and their properties. Some key questions asked about:
- Finding the degree of polynomials
- Identifying the number of real zeros of polynomials
- Factoring polynomials
- Evaluating polynomials for given values
- Identifying coefficients and constants in polynomial expressions
- Relating the zeros of a polynomial to its factors
The questions cover topics like polynomial definitions, operations, factorization, finding zeros, and other properties of polynomials.
Paso 2 profundizar y contextualizar el conocimiento de la unidad 1 ff
This document provides an overview of algebraic expressions and factorization techniques covered in Unit 1. It defines basic algebraic expressions, polynomials, monomials, binomials, trinomials and more. It then describes 10 cases of factorization, including common factors, difference of squares, sum/difference of cubes, and more. Examples are provided for each case to demonstrate the factorization processes.
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The document defines algebraic expressions and provides examples of basic operations - addition, subtraction, multiplication, and division - that can be performed on algebraic expressions. It also covers evaluating algebraic expressions for given variable values and important algebraic identities called "notable products", including differences and sums of squares and cubes. Examples are given for each type of operation and identity.
factoring trinomials the ac method and making lists
This document discusses factoring trinomials. It defines a trinomial as a three-term polynomial of the form ax2 + bx + c, where a, b, and c are numbers. There are two types of trinomials: those that are factorable, which can be written as the product of two binomials, and those that are prime or unfactorable. The document outlines the basic rules for factoring trinomials and provides an example of expanding a binomial expression into a trinomial.
Algebra unit 8.7
This document provides examples and explanations for factoring special cases of polynomials, including perfect square trinomials and the difference of two squares. It includes examples of recognizing, factoring, and explaining if expressions are in one of these forms. One example problem finds the perimeter of a garden given its area as a factored expression and evaluates the perimeter for a given value of x.
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Expresiones algebraicas pdf
This document discusses algebraic expressions, factorization, and radicals. It defines algebraic expressions and outlines rules for multiplying, dividing, and factoring algebraic expressions using notable products such as the difference of squares, sum and difference of cubes, and binomial squares. It also covers simplifying fractional algebraic expressions and operations involving fractions. Finally, it discusses factoring polynomials using the Ruffini method and summarizes rules for adding, subtracting, multiplying, and dividing radicals.
Expresiones algebraicas y factorizacion
Suma, resta y valor numérico de expresiones algebraicas.
multiplicación y división.
Producto notable de expresiones algebraicas.
Factorización por producto notable.
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The document discusses algebra and its basic concepts. It begins by introducing algebra and defining it as the aspect of mathematics involving the use of numbers and letters. It then provides examples of solving algebraic puzzles using letters to represent unknown numbers. The document goes on to define key algebraic terms like constants, variables, coefficients and terms. It also outlines fundamental algebraic rules like commutativity, associativity and distributivity. It discusses how to collect like terms and factorize expressions. Finally, it covers topics like expanding and simplifying brackets, fractions and factorizing expressions.
Produccion escrita expresiones algebraicas
The document discusses various algebraic operations including:
1) Summing algebraic expressions by adding like terms.
2) Subtracting algebraic expressions by adding the opposite of like terms.
3) Multiplying algebraic expressions by multiplying each term in one factor by each term in the other factor.
4) Dividing algebraic expressions using long division.
Bonus math project
This document provides an overview of different methods for solving quadratic equations, including factoring, graphing, using the quadratic formula, and more. It begins by defining the general and standard forms of quadratic equations. It then explains how to write equations in standard form and discusses concepts like the vertex, completing the square, determining zeroes/roots, and the discriminant. Finally, it reviews several methods that can be used to find roots of quadratic and higher-order polynomial equations, such as factoring, graphing, the quadratic formula, synthetic division, and the remainder/factor theorems.
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This document discusses two special cases for multiplying binomials: difference of squares and perfect square trinomials. For difference of squares, multiplying (a + b)(a - b) results in a^2 - b^2. For perfect square trinomials, squaring a binomial (a + b)^2 follows the pattern of a^2 + 2ab + b^2. Some examples are worked out applying these rules.
Similar to Special factor patterns (20)
Las expresiones algebraicas y Factorización de productos notables
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Expresiones Algebraicas, Factorización y Radicación.
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Joshua W. Zagorski is a math teacher at Cinnaminson Township Public Schools in New Jersey. He has over 10 years of experience teaching mathematics at the middle and high school levels. He holds a Master's degree in Education from La Salle University and a Bachelor's degree in Sociology from Moravian College. Zagorski has received several honors for his teaching, including being named Teacher of the Year at Cinnaminson Middle School. He actively integrates technology into his classroom and has led initiatives to supplement math instruction.
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Special factor patterns
- 2. 1. Write as a Binomial: (9-w)(9+w) 2. Write each square as a trinomial: (6c-1) ² 3. Simplify: (y+4)(y+10)
- 3. a ²-b² (a+b)(a-b) (First #)² - (Second #) ² = (sum of 2 squares) x (their difference)
- 4. Ex: 9a ² -4b ² =( 3a + 2b )(3a-2b) 3a is the square root of 9a ² and 2b is the square root of 4b ²
- 5. Ex: 36-25
- 6. 81-16 *** After you factor the number the first time, if there still is an a ²-b² in the subtraction binomial, you have to factor again until there are no squares left. ***
- 7. a ²+(-)2ab+b² (a+(-)b)² If the middle number in the equation equals twice the square root of a times the square root of b, then you can factor it.
- 8. Ex: a ² +2a+1 = ( a+1 ) ² a and 1 are the square roots of the first and last numbers
- 9. Ex: u ² -6u+9
- 10. Ex: b ² +12b+4 This trinomial can’t be factored this way because the middle number does not equal twice the product of the first and last number.
- 11. Ex: 121c^4-264c ² +144 ^4 means to the fourth power****
- 12. x²+(-)bx+c (x + factor of b that adds to c) (x +(-) factor of b that adds to c)
- 13. Ex: x ² +8x+15 = (x+ 3 ) (x+ 5 ) 5 and 3 add up to 8, and are a factor pair of 15.
- 14. Ex: x ² -10x+24
- 15. Ex: y ² +20yz+91z ²
- 16. Ex: x^4-15x ² y ² -16y^4