Question

PLEASE HELPPPP it's urgent!!

(PART A)
12x²+18x-12
Factor completely.
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(PART B)
Check your work from Part A by multiplying.

* YOU MUST SHOW ALL WORK FOR CREDIT *

Answer 1

12
`x^(2)` + 18x - 12

Before we get started, notice that 12 and 18 are both divisible by 6. This will be helpful when factoring!

Part A:

factor out 6

6(2
`x^(2)` + 3x -2)

So I need to figure out 2 numbers that multiply together and make -2 (only -2 and 1 OR 1 and -2) and also notice that we have a coefficient of 2 on that x^2, so... honestly this is sort of a game of guess & check, but we will have 1 set of parentheses with + and another with - because the middle term is positive and the last term is negative.

Now rewrite:

6(2x-1)(x+2)

Part B:

Let's check by expanding:

6(2x-1)(x+2)

6(2
`x^(2)`+4x-x-2)

Combine like terms

6(2
`x^(2)`+3x-2)

Now multiply everything in parentheses times 6:

12
`x^(2)`+18x-12

which was the original equation, so our factored equation is correct.