Use the remainder Theorem to find the remainder when
P(x) = x^4 - 9x^3 - 5x^2 - 3x + 4 is divided by x+3
The remainder theorem states that if a polynomial P(x) is divided by x – c, then the remainder is P(c).
In this case, we are dividing P(x) = x^4 - 9x^3 - 5x^2 - 3x + 4 by x + 3.
So, according to the remainder theorem, the remainder when P(x) is divided by x + 3 is P(-3).
Substituting -3 for x in P(x), we get:
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
= -194
Therefore, the remainder when P(x) is divided by x + 3 is -194.