Unit 2: Expressions and Polynomials GCF and Factoring

GCF Greatest Common Factor The largest factor in common between two numbers Ex: The GCF between 25 and 30 is 5 Ex: The GCF between 4x and 10 is 2 Ex: The GCF between 5mnp and 15mp is 5mp

GCF and Factoring Factor the GCF out of the following polynomial

Factoring Polynomials Review:

Factoring Polynomials Bottoms Up! To factor polynomials in the form Use the Bottoms Up Method This method works for factoring any type of polynomial!

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

Factoring Polynomials: Bottoms Up! Example: Factor Step 1: Multiply a and c together 1 x 45 = 45 Step 2: Two numbers that multiply to give 45 and add to give 14 9 and 5 Step 3: Place each number inside of binomials (x + 9) (x + 5) Step 4: Divide each of the constants by a a 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 together 2 x 18 = 36 Step 2: Two numbers that multiply to give 36 and add to give 15 12 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)