Question

$3 ^{4} + 6x ^{3} + 4x ^{2} + 8x$which of the following shows the factorization

Answer 1

Options A and D represents third degree polynomials, then, since our polynomial is a fourth degree polynomial it can't be those options. Let's expand options B and C and compare to our polynomial

$P(x)=3x^4+6x^3+4x^2+8x$

Expanding the option B:

$x(3x^2+4)(x-2)=(3x^3+4x)(x-2)=3x^4-6x^3+4x^2-8x$

This is not our polynomial. Expanding option C:

$x(3x^2+4)(x+2)=(3x^3+4x)(x+2)=3x^4+6x^3+4x^2+8x$

This is our polynomial! Our answer is option C.