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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) is divided by x + 3, we can use the Remainder Theorem which states that if a polynomial P(x) is divided by (x - a), then the remainder is P(a).
In this case, a = -3.
So, we substitute x = -3 into P(x):
P(-3) = (-3)^4 - 9(-3)^3 - 5(-3)^2 - 3(-3) + 4
P(-3) = 81 + 243 - 45 + 9 + 4
P(-3) = 292
Therefore, the remainder when P(x) is divided by x + 3 is 292.