Unit 2: Expressions and Polynomials

Unit 2: Expressions and PolynomialsGCF and Factoring

GCFGreatest Common FactorThe largest factor in common between two numbers

Ex: The GCF between 25 and 30 is 5Ex: The GCF between 4x and 10 is 2Ex: The GCF between 5mnp and 15mp is 5mp

GCF and FactoringFactor the GCF out of the following polynomial

Factoring PolynomialsReview:

Factoring Polynomials Bottoms Up!To factor polynomials in the form

Use the Bottoms Up MethodThis method works for factoring any type of polynomial!

Bottoms Up! StepsStep 1: Multiply a and c togetherStep 2: Find 2 number that multiply to give (ac) and add to give bStep 3: Place each of those numbers inside of separate binomials with x at the beginningStep 4: Divide each of the constants by aStep 5: If any constant is in fraction form, multiply each term in that binomial by the denominator

Factoring Polynomials: Bottoms Up!Example:FactorStep 1: Multiply a and c together1 x 45 = 45Step 2: Two numbers that multiply to give 45 and add to give 149 and 5Step 3: Place each number inside of binomials(x + 9) (x + 5)Step 4: Divide each of the constants by aa equals 1, so there is no need to divide further.

Your answer is (x + 9)(x + 5)

Factoring Polynomials: Bottoms Up!Factor the following polynomial:

Step 1: Multiply a and c together2 x 18 = 36

Step 2: Two numbers that multiply to give 36 and add to give 1512 and 3

Step 3: Place each number inside of binomials(x + 12) (x + 3)

Factoring Polynomials: Bottoms Up!Step 4: Divide each of the constants by

Step 5: Since is not an integer, multiply the 2nd binomial by 2 to get rid of the fraction.

Your final answer is

Try!Factor the following:1)

2)