Question

Find the remainder when x³+3x²+x+1 is divided by x+2. [Note:- use remainder theorem]
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Answer 1

Step-by-step explanation:

"(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."

Answer 2

Step-by-step explanation:

We can also say that x + 1 is a factor of x3 + 3x2 + 3x + 1. (ii) The root of x - (1/2) = 0 is 1/2. Hence by the remainder theorem, 27 / 8 is the remainder when x3 + 3x2 + 3x + 1 is divided by x. Hence by the remainder theorem, 1 is the remainder when x3 + 3x2 + 3x + 1 is divided by x.