Answer to Question #107973 in Algebra for Amy Wang

Question

For a polynomial p(x), the value of p(3) is −2. Which of the following must be true about p(x)?

A) x−5 is a factor of p(x).
B) x−2 is a factor of p(x).
C) x+2 is a factor of p(x).
D) The remainder when p(x) is divided by x−3 is −2.

Answer 1

Supose, we can factorize the polynomial as the following:

$p_n(x) = (x - 3)q_{n-1} + b,$

where $q_{n-1}$ is the polinomial of lower order and $b$ is the reminder.

Then, according to the initial condition:

$p_n(3) = 0\cdot q_{n-1} + b = -2.\\$

Thus, the reminder $b = -2$ when p(x) is divided by x−3.

Answer. D.