Question

x³+ 3x³+3x+1. by X+1. with long division
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Answer 1

Let p(x) be any polynomial of degree greater than or equal to one and let 'a' be any real number.

If a polynomial p(x) is divided by x - a then the remainder is p(a).

Let p(x) = x3 + 3x2 + 3x + 1

(i) The root of x + 1 = 0 is -1

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

= -1 + 3 - 3 + 1

= 0

Hence by the remainder theorem, 0 is the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1. We can also say that x + 1 is a factor of x3 + 3x2 + 3x + 1.

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