The factors of $x^{4} + 4$ are

{(x^{2} + 2)}^{2}

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(x^{2} + 2) {(x^{2} - 2)}^{2}

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(x^{2} + 2 x + 2) (x^{2} - 2 x + 2)

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{(x^{2} - 2)}^{2}

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Solution

The correct option is C $(x^{2} + 2 x + 2) (x^{2} - 2 x + 2)$
$\Rightarrow x^{4} + 4$
$\Rightarrow x^{4} + 4 x^{2} - 4 x^{2} + 4$
$\Rightarrow (x^{4} + 4 x^{2} + 4) - 4 x^{2}$
$\Rightarrow {(x^{2} + 2)}^{2} - (2 x)^{2}$
$\Rightarrow (x^{2} + 2 - 2 x) (x^{2} + 2 + 2 x)$
$\Rightarrow (x^{2} - 2 x + 2) (x^{2} + 2 x + 2)$

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Similar questions

The expresssion $x^{4} + 4$ can be factorized as

Q. The expression x⁴ + 4 can be factorized as

(a) (x² + 2x + 2) (x² − 2x + 2)

(b) (x² + 2x + 2) (x² + 2x + 2)

(c) (x² − 2x − 2) (x²− 2x + 2)

(d) (x² + 2) (x² − 2)

Which of the following is not a quadratic equation?
(a) $3 x - x^{2} = x^{2} + 5$
(b) $(x + 2)^{2} = 2 (x^{2} - 5)$
(c) $(2 x + 3)^{2} = 2 x^{2} + 6$
(d) $(x - 1)^{2} = 3 x^{2} + x - 2$

Subtract: 2 x^{2} + 6 - 4 x from 3 x^{2} - 6 x + 8.

Q. Subtracting

2 x^{2} + 6 - 4 x

from

3 x^{2} - 6 x + 8

gives .

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The factors of x4+4 are

The correct option is C (x2+2x+2)(x2−2x+2)⇒x4+4⇒x4+4x2−4x2+4⇒(x4+4x2+4)−4x2⇒(x2+2)2−(2x)2⇒(x2+2−2x)(x2+2+2x)⇒(x2−2x+2)(x2+2x+2)

The factors of $x^{4} + 4$ are