Using the factors $( x + 4 )$ and $( x + 3 )$, find the remaining factor(s) of $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12$ and write the polynomial in fully factored form.
A) $f ( x ) = ( x + 4 ) ( x + 3 ) ( x - 1 )$
B) $f ( x ) = ( x + 4 ) ( x + 3 ) ^ { 2 }$
C) $f ( x ) = ( x + 4 ) ( x + 3 ) ( x + 1 )$
D) $f ( x ) = ( x + 4 ) ^ { 2 } ( x + 3 )$
E) $\quad f ( x ) = ( x + 4 ) ( x + 3 ) ( x + 3 )$

Question

Quizplus · Accepted Answer

To find the remaining factor(s), we can use polynomial long division or synthetic division. Using either method, we find that dividing $f(x)$ by $(x+4)(x+3)$ leaves a quotient of $x-1$, which means the fully factored form of $f(x)$ is $(x+4)(x+3)(x-1)$. Therefore, the correct choice is A.

Using the Factors (x+4)( x + 4 )(x+4) And (x+3)( x + 3 )(x+3)

Using the Factors $( x + 4 )$ And $( x + 3 )$