Question

FIND THE REMAINDER WHEN X^3+3X^2+3X+1 IS DIVIDED BY X+1.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

          0

Step-by-step explanation:

By the Remainder Theorem, the remainder when f(x) is divided by x-a is just f(a).

So the remainder when f(x) = x³+3x²+3x+1 is divided by x+1 = x-(-1) is:

       f(-1) = (-1)³ + 3×(-1)² + 3×(-1) + 1  =  -1 + 3 - 3 + 1  =  0.

That is, the remainder is 0.

Alternatively, recognize this expansion from the Binomial Theorem:

   x³ + 3x² + 3x + 1  =  (x + 1)³