Polynomials and Factoring Module 6 Polynomials and Factoring

6.1 – Introduction and review of polynomials

Classify polynomials by term and degree

Prefixes – Classification by terms Mono – one term Bi – two terms Tri – three terms Poly – more than three terms (literally means: many)

Classification by Degrees The degree of a polynomial is the SUM of the exponents (including no visible exponents, which is an invisible 1) of the highest term. Examples: (2+1 = 3) (3+12 = 15) 2 1 (4+2 = 6) (3+3 = 6) 2 4

Standard Form of a Polynomial Standard form means that all of the exponents are in DESCENDING order (largest to smallest)

6.2 Operations of polynomials

Adding Polynomials Combine like terms (same exponent) Make sure you keep the sign (+ or -) that is in front of each term

Subtracting Polynomials Distribute the negative to everything in the second set of parentheses Combine like terms (same exponent) Make sure you keep the sign (+ or -) that is in front of each term

Multiplying Polynomials Monomial by a Polynomial Distribute the first polynomial to all terms in the parentheses Multiply the coefficients (big number before the variable) and add the exponents

Multiplying Polynomials Binomial by a Binomial Distribute the first term to all terms in the second parentheses Distribute the second term to all terms in the second parentheses Combine like terms

Multiplying Polynomials More terms? Just follow the steps and combine like terms! Make sure you pay attention to the signs and follow PEMDAS!

6.03 Factoring

Factoring out the GCF Find what number and/or variables ALL of the terms have in common Divide out the common factor GCF goes in front of the parentheses, and whatever is left after dividing goes in the parentheses

Difference of Squares

Perfect Square Trinomial

Other special cases