Question

determine whether the binomial expression is a factor to the following polynomial.$p(x) = {x}^{3} - 9x + 1 \: \: \: \: \: \: \: \: \: (x - 3)$the binomial expression is (x-3) ^^answer choicesA. yesB. no

Answer 1

We can find if (x-3) is a factor by dividing P(x) by (x-3).

A simpler way is replacing x with 3 and if the value of P(x) is 0, then (x-3) is a factor of P(x). This is because x=3 is a root of P(x) and therefore it can be factorized with the term (x-3).

Then, we calculate P(3):

$P(3)=3^2-9\cdot3+1=9-27+1=-17$

As x=3 is not a root of P(x), then (x-3) is not a factor of P(x).

Answer: No.