Question

Statement 1: (x-a) is a factor of p(x) if p(a) = 0.

Statement 2: If p(x) is divided by (x+a), remainder is equal to p(a).

• A. Both statements are correct and statement 2 explains statement 1.
• B. Both statements are correct but statement 2 does not explain statement 1.
• C. Only statement 1 is correct.
• D. Only statement 2 is correct.

Answer 1

The correct option is C Only statement 1 is correct.

According to remainder theorem, if p(x) is divided by (x-a), then remainder equals p(a). In statement 2, p(x) is divided by (x+a), so the remainder is equal to p(-a). Hence, statement 2 is wrong.

If remainder is zero, then (x-a) is a factor of p(x). But the remainder is p(a). So, p(a) = 0 is sufficient to prove that (x-a) is a factor of p(x). This is also known as the factor theorem.