Find the Quotient and the Remainder when the first polynomial is divided by the second.
$(x^{3} + 1)$ by $(x + 1)$

Quotient

= x^{2} - x + 1

, Remainder = 1

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Quotient

= x^{3} - x + 1

, Remainder = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Quotient

= x^{2} - x + 1

, Remainder= 0

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Quotient

= x^{3} - x + 1

, Remainder = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A Quotient $= x^{2} - x + 1$ , Remainder= 0
$\frac{(x^{3} + 1)}{(x + 1)}$

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

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

$= (x^{2} - x + 1)$
Quotient $= x^{2} - x + 1$
Remainder $= 0$

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