Question

If p(x) is divided by (x-c) with a remainder of 3, for what value of x is p(x) equal to 3?

A) x = c
B) x = c + 3
C) x = c - 3
D) x = 3
E) x = 0

Answer 1

The value of x for which p(x) is equal to 3 when divided by (x-c) with a remainder of 3 is x = c.

Step-by-step explanation:

To find the value of x for which p(x) is equal to 3 when divided by (x-c) with a remainder of 3, we can set up the equation p(x) = (x-c)q(x) + 3, where q(x) is the quotient.

Since p(x) is equal to 3, we have 3 = (x-c)q(x) + 3.

Subtracting 3 from both sides gives 0 = (x-c)q(x).

Since the remainder is 3 when p(x) is divided by (x-c), it means that (x-c)q(x) must be divisible by (x-c) with a remainder of 3. This is only possible if (x-c) equals 0, so the value of x is c, option A.