Using the factors (x - 4) and (x + 2), find the remaining factor(s) of $f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24$ and write the polynomial in fully factored form.
A) $f ( x ) = ( x - 4 ) ( x + 2 ) ^ { 2 }$
B) $f ( x ) = ( x - 4 ) ( x + 2 ) ( x + 3 )$
C) $f ( x ) = ( x - 4 ) ( x + 2 ) ( x + 7 )$
D) $f ( x ) = ( x - 4 ) ^ { 2 } ( x + 2 )$
E) $f ( x ) = ( x - 4 ) ( x + 2 ) ( x - 3 )$

Question

Quizplus · Accepted Answer

Given the factors (x - 4) and (x + 2), we can divide $f(x) = x^3 + x^2 - 14x - 24$ by these factors to find the remaining factor. Dividing $f(x)$ by (x - 4)(x + 2) yields a quotient of (x + 3), making the fully factored form $f(x) = (x - 4)(x + 2)(x + 3)$.

Using the Factors (X - 4) and (X + 2) f(x)=x3+x2−14x−24f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24f(x)=x3+x2−14x−24

Using the Factors (X - 4) and (X + 2) $f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24$