Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

Answer 2

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