Using the factors (x - 5)and (x + 2),find the remaining factor(s)of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - x + 30$ and write the polynomial in fully factored form.
A) $f ( x ) = ( x - 5 ) ( x + 2 ) ( x - 3 )$
B) $f ( x ) = ( x - 5 ) ( x + 2 ) ^ { 2 }$
C) $f ( x ) = ( x - 5 ) ( x + 2 ) ( x + 3 )$
D) $f ( x ) = ( x - 5 ) ^ { 2 } ( x + 2 )$
E) $f ( x ) = ( x - 5 ) ( x + 2 ) ( x + 1 )$

Question

Quizplus · Accepted Answer

Given the factors (x - 5) and (x + 2), we can divide $f(x) = x^3 - 6x^2 - x + 30$ by these factors to find the remaining factor. The polynomial can be factored as $f(x) = (x - 5)(x + 2)(x - 3)$, which simplifies to the given cubic function when expanded.

Using the Factors (X - 5)and (X + 2),find the Remaining