Which of the following is not a factor of x2-1x2- 8 -3x2- 3x2-

X^2+1x^2+ 8 +3x^2+ 3x^2 = 4x^2+4x^2+8 = (2x)^2+(2x)^2+(2×2x×2x) = (2x+2x)^2 = 2^2(x+1x)^2 = 4(x+1x)^2 Thus, nbsp;x+1x, nbsp;(x+1x)^2, 4 are factors of nbs ...

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Byju's Answer

Standard VIII

Mathematics

Factorisation by Common Factors

Which of the ...

Question

Which of the following is not a factor of $x^{2} + \frac{1}{x^{2}} + 8 + \frac{3}{x^{2}} + 3 x^{2}$ ?

x^{2} + \frac{1}{x^{2}}

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(x + \frac{1}{x})^{2}

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x + \frac{1}{x}

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Solution

The correct option is A $x^{2} + \frac{1}{x^{2}}$
$x^{2} + \frac{1}{x^{2}} + 8 + \frac{3}{x^{2}} + 3 x^{2}$
= $4 x^{2} + \frac{4}{x^{2}} + 8$
= $(2 x)^{2} + (\frac{2}{x})^{2} + (2 \times 2 x \times \frac{2}{x})$
= $(2 x + \frac{2}{x})^{2}$
= $2^{2} (x + \frac{1}{x})^{2}$
= $4 (x + \frac{1}{x})^{2}$
Thus, $x + \frac{1}{x}, (x + \frac{1}{x})^{2}, 4$ are factors of $x^{2} + \frac{1}{x^{2}} + 8 + \frac{3}{x^{2}} + 3 x^{2}$ , while $x^{2} + \frac{1}{x^{2}}$ is not.

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Which of the following is not a factor of x2+1x2+8+3x2+3x2?

The correct option is A x2+1x2x2+1x2+8+3x2+3x2 = 4x2+4x2+8 = (2x)2+(2x)2+(2×2x×2x) = (2x+2x)2 = 22(x+1x)2 = 4(x+1x)2 Thus, x+1x,(x+1x)2,4 are factors of x2+1x2+8+3x2+3x2, while x2+1x2 is not.

Which of the following is not a factor of $x^{2} + \frac{1}{x^{2}} + 8 + \frac{3}{x^{2}} + 3 x^{2}$ ?