Find the remainder when $ f(x) = x^6 + 5x^2 - x^3 + x - 6 $ is divided by $ (x + 1) $.

Question

9. Find the remainder when $ f(x) = x^6 + 5x^2 - x^3 + x - 6 $ is divided by $ (x + 1) $.

SnapAndSolve AI · Accepted Answer

To find the remainder when a polynomial $ f(x) $ is divided by $ (x + 1) $, use the Remainder Theorem. Substitute $ x = -1 $ into $ f(x) $:

$ f(-1) = (-1)^6 + 5(-1)^2 - (-1)^3 + (-1) - 6 $

$ = 1 + 5 + 1 - 1 - 6 $

$ = 0 $

Therefore, the remainder is 0.

Find the remainder when \( f(x) = x^6 + 5x^2 - x^3 + x - 6 \) is divided by \( (x + 1) \).