There are many ways that you can factor this out. I'd recommend and personally use the grouping method - this way once you get the concept down, you got it and you don't need to guess and check all the time. Another plus is that factoring 4 terms are much easier.
Now, get your hard hats on. Time to factor.
1st: Multiply a and the c term. Now, factor out the number you got from multiplying a and c. The two factors must add up to equal what b is.
12x^2 + 5x - 2
Factor of 24 that when added equals to 5: 8 and -3 (8 + -3 = 5)
12x^2-3x+8x-2
Now, look at it like this:
12x^2-3x 8x-2
Then factor each separately:
3x(4x - 1) + 2(4x - 1)
Afterwards, form your answer.
(3x + 2) (4x - 1)
4x^2 - 4x + 1
Factors of 4 (4x1) that when added equal 4: -2 and -2 which equal - 4
4x^2 - 2x - 2x + 1
2x(2x - 1) - 1 (2x - 1)
Answer: (2x - 1)(2x - 1) or (2x - 1)^2
3x^2 - 3x - 90
Factors of 270 (3x90) that when added equal 3: -18 and 15 which equal - 3
3x^2 + 15x - 18x - 90
3x(x + 5) - 18(x + 5 )
Answer: (3x - 18) (x + 5)
