Which of the following is a factor of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 8$
A) x+4
B) x+8
C) x-4
D) x-8

Name: Which of the following is a factor of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 8$ A) x+4 B) x+8 C) x-4 D) x-8
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Question

Quizplus · Accepted Answer

The factor theorem states that if $x-c$ is a factor of a polynomial $P(x)$, then $P(c)=0$. For $x-4$ to be a factor, $P(4)$ must equal 0. Substituting 4 into the polynomial gives $4^3 - 5(4)^2 + 6(4) - 8 = 0$, confirming that $x-4$ is a factor.

Which of the Following Is a Factor Of P(x)=x3−5x2+6x−8P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 8P(x)=x3−5x2+6x−8

Which of the Following Is a Factor Of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 8$