Introduction to Factoring Lesson 19 Instructional Material 2

Example 1 12a2 + 16a = 4a(3a + 4)

Example 2 15x + 25x2 = 5x(3 + 5x)

Example 3 7x4 + 14x5 + 21x3 = 7x3 (x +2x2 + 3)

Example 4 18cd2 + 12c2d + 9cd = 3cd(6d + 4c + 3)

Example 5 4x5y- 2x3y2 + 6xy3 = 2xy(2x4 – x2y + 3y2)

Factoring trinomials: Review: Trinomials have 3 terms In the form: ax2+bx+c Where a, b, and c are numbers Also in the form: x2+bx+c Where the leading coefficient is 1

Factoring trinomials: You can factor any trinomial by following these steps! 1.) Look for a GCF 2.) Multiply the first number and the last number 3.) Find the factors of that number (step 2) that add up to the middle term in the trinomial 4.) Replace the middle term with the factors found in step 3 5.) Factor the 4 terms by grouping 6.) Factor each parenthesis (Find the GCF of each parenthesis)

Let’s try it! x2 + 7x + 12 This is a trinomial in the form x2 + bx + c 1.) Find the GCF This trinomial doesn’t have a GCF, because the leading coefficient is 1. So go on to Step 2. 2.) Multiply the first and last number 1 x 12 = 12 3.) Find the factors of 12 that add up to 7 1 x 12 = 12 → 1 + 12 = 13 2 x 6 = 12 → 2 + 6 = 8 3 x 4 = 12 → 3 + 4 = 7

Cont. x2 + 7x + 12 4.) Replace the middle term with the factors found in step 3 x2 + 3x + 4x + 12 5.) Factor the 4 terms by grouping (x2 + 3x) + (4x + 12) 6.) Factor each parenthesis x (x + 3) + 4 (x + 3) (x+3) (x + 4)

Example 2: X2 -10x + 24 1.) No GCF. 2.) 1 x 24 = 24

Cont. X2 -10x + 24 4.) X2 - 6x - 4x + 24 5.) (X2 - 6x) – (4x + 24)

Example 3: X2 - 4x – 21 1 x – 21 = - 21 -7 x 3 = - 21 and -7 + 3 = -4