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Chapter 7: Q. 402 (page 899)

Factor Trinomials Using the 鈥渁c鈥� Method.

In the following exercises, factor.

15x2+x-2

Short Answer

Expert verified

15x2+x-2=(3x-1)(5x+2)

Step by step solution

01

Step 1. Given information

We have been given a trinomial 15x2+x-2.

We have to factor it Using the 鈥渁c鈥� Method.

02

Step 2. Find the product ac 

15x2+x-2a=15c=-2ac=15(-2)=-30

03

Step 3. Find two numbers m and n that m⋅n=a⋅c  and  m+n=b

We have to find m and n such that:

m鈰�n=-30andm+n=1

Therefore, we get:

m=6n=-5

04

Step 4. Split the middle term using m and n and then factor by grouping. 

15x2+x-2=15x2+6x-5x-2=3x(5x+2)-1(5x+2)=(3x-1)(5x+2)

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