Question

how do you do this by using the FOIL method?

1. 3x^2 + 22x + 7=


2. 2x^2 + 5x - 12=

3. x^2 - 11x + 28=

thank you!

Answer 1

FOIL is an acronym to find the product of 2 binomials.
What you want is the reverse of that method, you want to factor it back into the 2 binomials.

I used to teach about 3 different ways to do this, the popular one these days appear to be "decomposition"

I will do #2
step 1: multiply the first and last coefficients:
2(-12) = -24
step 2: find two numbers which have a sum of the middle term coefficient, which is 5 and have a product of -24
how about 8 and -3 , ( 8(-3) = -24 and 8-3=5)

so "decompose" the middle term of 5x to 8x-3x

2x^2 - 3x + 8x - 12
now factor in pairs...
= x(2x-3) + 4(2x-3) , You MUST now have a pair of equal factors , in this case 2x-3

= (2x-3)(x+4)