Question

For a polynomial p(x), p(2) = p(5). Choose the correct alternatives.

• A. The values of the p(x) at x = 2 and x = 5 is the same.
• B. The remainders of p(x) when divided by (x-2) and (x-5) is the same.
• C. The quotients of p(x) when divided by (x-2) and (x-5) is the same.
• D. (x-2) and (x-5) are factors of p(x).

Answer 1

Answer: (A), (B)

The correct options are
A The values of the p(x) at x = 2 and x = 5 is the same.
B The remainders of p(x) when divided by (x-2) and (x-5) is the same.

The value of the polynomial p(x) at x = 2 is also written as p(2).
Since p(2) = p(5), the values of p(x) at x = 2 and x = 5 are the same.

According to remainder theorem,
When p(x) is divided by (x-2), the remainder is equal to p(2).
When p(x) is divided by (x-5), the remainder is equal to p(5).
p(2) = p(5). Hence, the remainders are the same.

For (x-2) to be a factor, p(2) should be equal to zero. However, no such information is given. Same argument holds for (x-5).