Question

Find the remainder when x3 + 3x2 + 3x + 1 is divided by
x + 1​

Answer 1

Answer:

x+1 ) x^3 + 3x^2 + 3x +1 ( x^2 + 2x + 1

+x^3 + x^2

- -

__________

0 + 2x^2 + 3x +1

+ 2x^2 + 2x

- -

_____________

0 + x + 1

+ x + 1

- -

_________

0

the remainder will be 0

By another way ,

x+1 =0

x= (-1)

now evaluating the value of x

x^ 3 + 3x^2 + 3x + 1

(-1)^3 + 3(-1)^2 +3(-1) + 1

-1 +3 -3 +1

= 0

Hope it helps you

Answer 2

Answer:

The remainder is 0.

Step-by-step explanation:

Let p(x) = x³ + 3x² + 3x + 1

x+1 = 0 ⇒ x = -1

∴ Remainder

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

= -1 + 3 - 3 + 1

= 0

Therefore, The remainder is 0.