Determine if x-1 is a factor of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - x + 5$
A) factor
B) not a factor

Question

Quizplus · Accepted Answer

To determine if $x-1$ is a factor of $P(x)$, we can use the Remainder Theorem. According to the theorem, if $x-1$ is a factor of $P(x)$, then $P(1) = 0$. Substituting $x = 1$ into $P(x)$, we get $P(1) = 1^3 - 5(1)^2 - 1 + 5 = 1 - 5 - 1 + 5 = 0$. Since $P(1) = 0$, $x-1$ is indeed a factor of $P(x)$.

Determine If X-1 Is a Factor Of P(x)=x3−5x2−x+5P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - x + 5P(x)=x3−5x2−x+5

Determine If X-1 Is a Factor Of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - x + 5$