Question

What is the factorization of the trinomial below 12x^2-x-35

Answer 1

12x^2-x-35
12x^2-21x+20x-35
3x(4x-7)+5(4x-7)
(4x-7)(3x+5)
Either,
x=7/4
Or,
x=-5/3

Answer 2

`(4x-7)(3x+5)`

Explanation:

1) Looking attentively to
`12x^(2)-x-35`. We need two find two numbers whose product is
`(12)(-35)=-420` and their sum is -1.

2) These numbers are -21 and 20 their product is -420 and their sum is -1. Prime factorization might be a good start to find those numbers. Moreover, you can make a list of numbers whose product is -420.

3) Rewrite the trinomial, with those two terms as new b terms.

`12x^(2)-x-35=12x^(2)-21x+20x-35`

4) Finally, factor them by grouping them:

`(12x^(2)-21x)+(20x-35)\Rightarrow 3x(4x-7)+5(4x-7)\Rightarrow (4x-7)(3x+5)`