Question

Explain how the trinomial 2x2+ 13x + 15 can be turned into a four term polynomial suitable for factoring by grouping. Use complete sentences.

Answer 1

Multiply the 2 and the 15 and find factors of 30 whose sum is 13 and then rewrite 13x as the sum of those two numbers. For example, 10 x3 = 30 and 10 + 3 is 13 so replace 13x with 10x + 3x

Answer 2

2 * 15 = 30 - we need three factors which can be made to equal 13
- these are 2 , 3 and 5 ( 2*5 + 3)
so we write

2x^2 + 3x + 5x + 15
we need 2*5 so we factor as follows
2x(x+5) + 3(x+5)
= (2x + 3)(x + 5)

Answer 3

Now you have 2x^2+10x+3x+15
Factor it by grouping