Question

the polynomial expression $3n^{3}+n^{2}-12n - 4$ can be written as the product of $(3n + 1)$ and $f$
what is the value of $f$
a. $(n + 4)(n - 4)$
b. $(n + 2)(n - 2)$
c. $(n + 2)^{2}$
d. $n^{2}+4$

Explanation:

Step1: Group polynomial terms

$3n^3 + n^2 - 12n - 4 = (3n^3 + n^2) + (-12n - 4)$

Step2: Factor out common terms

$= n^2(3n + 1) - 4(3n + 1)$

Step3: Factor out $(3n+1)$

$= (3n + 1)(n^2 - 4)$

Step4: Factor difference of squares

$n^2 - 4 = (n + 2)(n - 2)$

Answer:

B. $(n + 2)(n - 2)$