Q1 of 86 Page 42

Find the remainder when x3 + 3x2 + 3x + 1 is divided by the following Linear polynomials:

x + 1

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


As we know by Remainder Theorem,


If a polynomial p(x) is divided by a linear polynomial (x – a) then, the remainder is p(a)


⇒ Remainder of p(x) when divided by x+1 is p(–1)


p(–1) = (–1)3 + 3(–1)2 + 3(–1) +1


⇒ p(–1) = –1 + 3 – 3 + 1 = 0


∴ Remainder of x3 + 3x2 + 3x + 1 when divided by x+1 is 0


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