Question

Find the Quotient and the Remainder when the first polynomial is divided by the second.

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

• A. Quotient $=x^2-x+1$, Remainder = 1
• B. Quotient $=x^3-x+1$, Remainder = 1
• C. Quotient $=x^2-x+1$, Remainder= 0
• D. Quotient $=x^3-x+1$, Remainder = 0

Answer 1

Answer: (C)

Quotient $=x^2-x+1$, Remainder= 0

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

Using the formula, $x^3+y^3=(x+y)(x^2-xy+y^2)$

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

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

Remainder $=0$