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

D

Explanation:

given polynomial p(x), the value of p(3) is −2

A) x−5 is a factor of p(x) is true only if p(5)=0

B) x−2 is a factor of p(x) is true only if p(2)=0

C) x+2 is a factor of p(x) is true only if p(-2)=0

so only choice left n is the correct ans:

D) The remainder when p(x) is divided by x−3 is −2.

Answer 2

D) The remainder when p(x) is divided by x−3 is −2.

Explanation:

If p(3) =-2 then (x-3) is not a factor of p(x)

If it were a factor then p(3) would equal 0

p(3) =-2 means than -2 is the remainder when you divide the function by (x-3)

by the Remainder theorem