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If $x^{2} - 2$ is a factor of $x^{4} + 2 x^{3} - 2 x^{2} - 4 x$ , find the other factor (the quotient).

Class 10Division AlgorithmAlgebra — Polynomials

A $x^{2} + 2 x$
B $x^{2} - 2 x$
C $x^{2} + 2$
D $x^{2} - 2$

Step-by-Step Solution

Dividing

x^{4} + 2 x^{3} - 2 x^{2} - 4 x

by

x^{2} - 2

gives

x^{2} + 2 x

with remainder 0. Check:

(x^{2} - 2) (x^{2} + 2 x) = x^{4} + 2 x^{3} - 2 x^{2} - 4 x

.

Answer: A)

x^{2} + 2 x

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