Answer:
The correct option is (3a+4)(a-6)
Step-by-step explanation:
We have the polynomial [tex]3a^2-14a-24[/tex]
For the polynomials of the form [tex]ax^2+bx+c[/tex] we have to rewrite the middle term as a sum of two terms whose product is, in this case, a.c=-72 and whose sum is b=(-14)
We have to factorize -14 from -14a:
[tex]3a^2-14(a)-24=\\3a^2-(18-4)(a)-24=\\=3a^2-18a+4a-24[/tex]
Because b=(-18)+4=(-14) and a.c=(-18).4=(-72)
Now we have to factor by grouping:
[tex]3a^2-18a+4a-24=\\(3a^2-18a)+(4a-24)=\\3a(a-6)+4(a-6)=\\=(3a+4)(a-6)[/tex]
Then, the correct option is (3a+4)(a-6)
