Answer:
[tex](4x-7)(3x+5)[/tex]
Step-by-step explanation:
1) Looking attentively to [tex]12x^{2}-x-35[/tex]. We need two find two numbers whose product is [tex](12)(-35)=-420[/tex] 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.
[tex]12x^{2}-x-35=12x^{2}-21x+20x-35[/tex]
4) Finally, factor them by grouping them:
[tex](12x^{2}-21x)+(20x-35)\Rightarrow 3x(4x-7)+5(4x-7)\Rightarrow (4x-7)(3x+5)[/tex]
