Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$x ^ { 3 } - 3 x ^ { 2 } + 7 x - 5 ; x - 1$
A) Yes
B) No

Question

Quizplus · Accepted Answer

The factor theorem states that a polynomial $f(x)$ has a factor $x - c$ if and only if $f(c) = 0$. Substituting $x = 1$ into the given polynomial $x^3 - 3x^2 + 7x - 5$, we get $1^3 - 3(1)^2 + 7(1) - 5 = 1 - 3 + 7 - 5 = 0$. Since the result is 0, $x - 1$ is a factor of the polynomial.

Use the Factor Theorem to Decide Whether or Not the Second