Question

Let V be the real vector space consisting of all polynomials in one variable with real coefficients and having degree at most 5, together with the zero polynomial. Let T: V-> $\R$ be the linear map defined by 7(1) = 1 and T(x(x-1)... (x-k+1)) = 1 for 1 ≤ k ≤ 5.
Then which of the following is/are true?

• A. T(x4) = 15.
• B. T(x3) = 15.
• C. T(x4) = 14.
• D. T(x3) = 3.

Answer 1

Answer: (A), (B)

T(x4) = 15.

Answer 2

The correct option is (A): T(x4) = 15. and (B): T(x3) = 15.