Polynomials WebQuest
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This document discusses the basics of polynomials. It defines a polynomial as the sum or difference of monomials, binomials, and trinomials, which contain variables, constants, and exponents. The document explains how to perform operations like addition, subtraction, multiplication, and division on polynomials. It discusses long division as a method for dividing polynomials and notes that polynomials can never be divided by a variable.
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Algebra is the use of symbols to represent values and their relationships. Key concepts in algebra include:
- Variables represent unknown values and are often represented by letters.
- Polynomials are expressions involving variables and coefficients with addition, subtraction, multiplication, and non-negative exponents.
- The degree of a polynomial refers to the highest exponent on any term.
- Important algebraic operations include addition, subtraction, multiplication, and factorization of polynomials.
- Systems of linear equations can be solved using several methods like substitution, elimination, and cross-multiplication. The consistency of the system determines if there is a unique solution, infinite solutions, or no solution.
Simplifying expressions
This document provides an overview of simplifying algebraic expressions. It discusses algebraic expressions and examples. The key skills covered are using the distributive property to simplify expressions involving grouping symbols and combining like terms. Examples are provided to demonstrate simplifying expressions using these skills along with evaluating expressions by substituting values for variables.
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Polynomials WebQuest
- 1. polynomials Jaden Broadnax Mrs. Bankston Math 3 Honors
- 2. thebasicsofpolynomials ➔ Polynomial can be broken down into “poly” and “-nomial”. ◆ poly ➼ “many” ◆ -nomial ➼ “term” ➔ A polynomial is the sum or difference of monomials, binomials, and trinomials. These polynomials can contain- ◆ constants ➼ a number on it’s own (ex. 3, -20, ½) ◆ variables ➼ a symbol for a number we don’t know yet (x, y) ◆ exponents ➼ a number that says how many times to use the value in multiplication (8² = 8 x 8 = 64) ➔ These polynomials can also be combined by various math operations. ◆ addition / subtraction ◆ multiplication ◆ division / long division ● a polynomial can never be divided by a variable
- 3. monomials,binomials,andtrinomials ➔ Other kind of expressions used are monomials, binomials, and trinomials. These kinds of expressions are labeled by the number of terms they each have. ◆ monomial ➼ 1 term ● 3xy² ◆ binomial ➼ 2 terms ● 5x - 1 ◆ trinomial ➼ 3 terms ● 3x + 5y² - 3 ➔ Polynomials can also have degrees. ◆ the degree of a polynomial with only one variable is the largest exponent of that variable ● 4x³ - x + 3 ➼ the degree of this polynomial is 3. ➔ Most polynomials are written in standard form, which means the terms are written in descending order. ◆ x⁶ + 4x³ + 3x² - 7
- 5. addingpolynomials ➔ To add polynomials, add any like terms together. ◆ like terms have the same variables (and their exponents) equation made using Daum Equation Editor
- 6. subtractingpolynomials ➔ To subtract polynomials, first reverse the sign of each term that is being subtracted, and then add as usual. equation made using Daum Equation Editor
- 7. multiplyingpolynomials ➔ To multiply 2 polynomials- ◆ multiply each term in one polynomial by each term in the other polynomial ◆ add those answers and simplify if needed ➔ There are many different possibilities when multiplying polynomials- ◆ 1 term x 1 term ● (2xy)(4y) = (2)(4)(xy)(y) ◆ 1 term x 2 terms ● 2x(x+2xy) = (2x + x) + (2x)(3xy) = 2x²+6x²y ◆ 2 terms x 2 terms (FOIL) ● (2x+3)(xz-a) ○ 2x²z-2xa+3xz-3a ◆ 2 terms x 3 terms ● (x+a) (2x+3y-5) ○ 2x²+3xy-5x+2ax+3ay-5a ➔ always remember to add like terms
- 8. dividingpolynomialspt.1;basicdivision ➔ Some polynomials can be divided using basic division. To do this, it’s easiest to split the equation at the “+” and “-” signs. equation made using Daum Equation Editor - this answer is not a polynomial, because it contains division by a variable
- 9. dividingpolynomialspt.1;usinglongdivision ➔ The top polynomial is the numerator, while the bottom polynomial is the denominator. ➔ The denominator is written first, while the numerator is written beneath the radical symbol. equation made using Daum Equation Editor
- 10. dividingpolynomials;methodsforlongdivision 01. Divide first term of the numerator by the first term of the denominator 02. Multiply the denominator by that answer, and that below the numerator 03. Subtract to create a new polynomial equation made using Daum Equation Editor - if a remainder is left, this number goes above the bottom polynomial in the final answer