The real factors of $x^{4} + 4$ are __________.

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

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

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

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Does not exist

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Solution

The correct option is C $(x^{2} - 2 x + 2) (x^{2} + 2 x + 2)$
Given expression is $x^{4} + 4$
Add and subtract $4 x^{2}$ in the given expression
$x^{4} + 4 = (x^{4} + 4 x^{2} + 4) - 4 x^{2}$
$= (x^{2} + 2)^{2} - (2 x)^{2}$
We know the identity $a^{2} - b^{2} = (a - b) (a + b)$
$x^{4} + 4 = (x^{2} + 2 + 2 x) (x^{2} + 2 - 2 x)$
Hence, justified.

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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)

${lim}_{x \to \sqrt{2}} \frac{x^{2} - 2}{x^{2} + \sqrt{2 x} - 4}$

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

Question 2
Which of the following is not a quadratic equation?
(a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
(b) $2 x - x^{2} = x^{2} + 5$
(c) ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

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The real factors of x4+4 are __________.

The correct option is C (x2−2x+2)(x2+2x+2)Given expression is x4+4Add and subtract 4x2 in the given expressionx4+4=(x4+4x2+4)−4x2=(x2+2)2−(2x)2We know the identity a2−b2=(a−b)(a+b)x4+4=(x2+2+2x)(x2+2−2x)Hence, justified.

The real factors of $x^{4} + 4$ are __________.