Question

Find the remainder when $x^3+3x^2+3x+1$ is divided $(x+1).$

• A. X + 1
• B. 0
• C. X
• D. $x+\pi$

Answer 1

Answer: (B)

0

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

$=(x^3+1)+3x(x+1)$

$=(x+1)(x^2-x+1)+3x(x+1)$

$=(x+1)(x^2-x+1+3x)$

$=(x+1)(x^2+1+2x)$

$=(x+1){(x+1)}^2$

$={(x+1)}^3$

Quotient$=\frac{x^3+3x^2+3x+1}{x+1}=\frac{{(x+1)}^3}{x+1}={(x+1)}^2$

$\therefore ,x^3+3x^2+3x+1={(x+1)}^2(x+1)+0$

Hence the ramainder$=0$