Use the Remainder Theorem to find the remainder when P(x)=x^4-9x^3-5x^2-3x+4 is divided by x+3.

How do I do this?

292 ?

f(x)/(x-a) = f(a)

here a = -3
so we need f(-3)

f(-3) =(-3)^4-9(-3)^3-5(-3)^2-3(-3)+4

= 81 + 9*27 - 45 +9 + 4

= 81 + 243 - 45 + 9 + 4

To find the remainder when a polynomial is divided by a linear factor, you can use the Remainder Theorem. The Remainder Theorem states that if a polynomial P(x) is divided by x - r (where r is a constant), the remainder is equal to P(r).

In this case, you want to find the remainder when P(x) = x^4 - 9x^3 - 5x^2 - 3x + 4 is divided by x + 3.

To use the Remainder Theorem, substitute -3 for x in the polynomial P(x) and compute the value:

P(-3) = (-3)^4 - 9(-3)^3 - 5(-3)^2 - 3(-3) + 4

Calculate this expression to find the remainder.

use synthetic division