Question

P(x)=3x 4 −2x 3 +2x 2 −1P, left parenthesis, x, right parenthesis, equals, 3, x, start superscript, 4, end superscript, minus, 2, x, cubed, plus, 2, x, squared, minus, 1 What is the remainder when P(x)P(x)P, left parenthesis, x, right parenthesis is divided by (x+1)(x+1)left parenthesis, x, plus, 1, right parenthesis?

Answer 1

The remainder when the polynomial is divided by x + 1 is 2

Given the function P(x)=3x^4 −2x^3 +2x^2 −1, to get the rmainder if the polynomial is divided by x + 1, we will substitute x = - 1 into the function to have:

P(-1) = 3(-1)^4 −2(-1)^3 +2(-1)^2 −1

P(-1) = 3(1) - 2 + 2(1) - 1

P(-1) = 1 + 1

P(-1) = 2

Hence the remainder when the polynomial is divided by x + 1 is 2

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