If -2x 3 6x 2 17x - 21 is divided by x 1 then t... - JAMB Mathematics 2023 Question

Given polynomial: \( p(x) = -2x^3 + 6x^2 + 17x - 21 \)

We want to find the remainder when \( p(x) \) is divided by \( (x + 1) \). According to the Remainder Theorem, if you substitute \( x = -1 \) into \( p(x) \), you get the remainder.

So, substitute \( x = -1 \) into \( p(x) \):

\[ p(-1) = -2(-1)^3 + 6(-1)^2 + 17(-1) - 21 \]

Simplify each term:

\[ p(-1) = -2(-1) + 6(1) - 17 - 21 \]

\[ p(-1) = 2 + 6 - 17 - 21 \]

\[ p(-1) = -30 \]

Therefore, the remainder is \(-30\).