Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the Remainder Theorem to find the remainder when P(x) = x4 – 9x3 – 5x2 – 3x + 4
is divided by x + 3
.
To find the remainder using the Remainder Theorem, we substitute -3 into the polynomial P(x) and evaluate it.
P(-3) = (-3)^4 - 9(-3)^3 - 5(-3)^2 - 3(-3) + 4
= 81 - 9(-27) - 5(9) + 9 + 4
= 81 + 243 - 45 + 9 + 4
= 292
Therefore, the remainder when P(x) is divided by x + 3 is 292.