MODULE 6 POLYNOMIALS AND FACTORING 6 1 INTRODUCTION

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 (4+2 = 6) (3+3 = 6) 2 4 1

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 expone

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