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 when P(x) = x^4 – 9x^3 – 5x^2 – 3x + 4 is divided by x + 3, we can use the Remainder Theorem.
The Remainder Theorem states that if P(x) is divided by x - a, then the remainder is equal to P(a). In this case, we need to find the remainder when P(x) is divided by x + 3, so we need to evaluate P(-3).
Let's substitute -3 for x in P(x) and find the value:
P(-3) = (-3)^4 – 9(-3)^3 – 5(-3)^2 – 3(-3) + 4
= 81 + 243 - 45 + 9 + 4
= 292
Therefore, the remainder when P(x) is divided by x + 3 is 292.