Question

Which of the following represents the factorization of the polynomial below ?

Answer 1

2x² + 13x + 15

First you multiply the first and last number, 2 · 15 = 30

Now you need to find the factors of 30 that add or subtract to +13(I added the plus sign to indicate that the factors that add/subtract to 13 must come out as positive 13)

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 [1 · 30, 2 · 15, 3 · 10, 5 · 6]

You can do either 15 and 2 because 15 - 2 = 13, or 3 and 10 because 3 + 10 = 13.

I will be doing 10 and 3

2x² + 13x + 15    Instead of 13x, you can replace it with 3x and 10x because when you add it together it is 13x

2x² + 3x + 10x + 15   Now you can factor them out separately

x(2x + 3) + 5(2x + 3) You can factor out (2x + 3) from x and 5 to get:

(2x + 3)(x + 5)