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When the polynomial p(x) = x^3+ ax^2+ bx+ 3 is divided by x+3, the remainder is 9.
a. Given that p(1) = 1. find a and b
b. Find the remainder when p(x) is divided by x-4

Respuesta :

coochieman1413

Answer:

a = 3, b = 8

Step-by-step explanation:

Since x+3 is a factor, x=-3 is a root. =>  f(−3)=2(−3)3+a(−3)2−b(−3)+3=0

=>  9a+3b=51   =>  3a+b=17 — (1)

x-2 leaves a reminder of 15 =>  f(2)=2(2)3+a(2)2−b(2)+3=15

=>4a−2b=−4=>2a−b=−2 —- (2)

Adding (1) & (2),  5a=15=>a=3

Substituting the value of a in (1),  b=8

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