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) $f ( x ) = ( x + 4 ) ( x + 3 ) ( x + 3 )$

Question

Quizplus · Accepted Answer

Given that $f(x) = (x + 4)(x + 3)$ are factors, we can divide $f(x)$ by these factors to find the remaining factor. Dividing $x^3 + 6x^2 + 5x - 12$ by $(x + 4)(x + 3)$ yields $x - 1$, making the fully factored form $f(x) = (x + 4)(x + 3)(x - 1)$.

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

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