Which among the following is not a factor of x2 -2x-2x3 - 1-

Let's factorize the given expression. x^2 – √(2)x + √(2)x^3 nbsp;– 1 = √(2)x^3+x^2 – √(2)x 1 = x^2(√(2)x+1) (√(2)x+ 1) = (x^2 1)(√(2)x+1) = (x 1)(x+1)(√(2)x ...

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Standard X

Mathematics

Quadratic Formula

Which among t...

Question

Which among the following is not a factor of $x^{2} - \sqrt{2} x + \sqrt{2} x^{3} - 1 ?$

x - 1

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\sqrt{2} x + 1

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x + 1

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\sqrt{2} x - 1

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Solution

The correct option is D $\sqrt{2} x - 1$
Let's factorize the given expression.
$x^{2} - \sqrt{2} x + \sqrt{2} x^{3} - 1$
$= \sqrt{2} x^{3} + x^{2} - \sqrt{2} x - 1$
$= x^{2} (\sqrt{2} x + 1) - (\sqrt{2} x + 1)$
$= (x^{2} - 1) (\sqrt{2} x + 1)$
$= (x - 1) (x + 1) (\sqrt{2} x + 1)$
$B y u s i n g a^{2} - b^{2} = (a + b) (a - b)$ , we have:
$x - 1, x + 1, \sqrt{2} x + 1$

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Which among the following is not a factor of x2−√2x+√2x3−1?

The correct option is D √2x−1Let's factorize the given expression. x2–√2x+√2x3–1 =√2x3+x2–√2x−1 =x2(√2x+1)−(√2x+1) =(x2−1)(√2x+1) =(x−1)(x+1)(√2x+1) By using a2−b2=(a+b)(a−b), we have: x−1,x+1,√2x+1

Which among the following is not a factor of $x^{2} - \sqrt{2} x + \sqrt{2} x^{3} - 1 ?$