If the HCF and the LCM of the polynomial are $x^{2}$ - 1, $x^{4}$ - 1 respectively. Find out the uncommon factor of the two polynomials.

x + 1

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x - 1

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$x^{2}$ + 1

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Solution

The correct option is D
$x^{2}$ + 1

LCM = HCF $\times$ Uncommon terms

Then by dividing a LCM by HCF of polynomials we get the required uncommon term.

Therefore, Uncommon term = $\frac{L C M}{H C F}$ = $\frac{x^{4} - 1}{x^{2} - 1}$ = $x^{2}$ + 1

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If the HCF and the LCM of the polynomial are x2 - 1, x4 - 1 respectively. Find out the uncommon factor of the two polynomials.

The correct option is D x2 + 1 LCM = HCF × Uncommon terms Then by dividing a LCM by HCF of polynomials we get the required uncommon term. Therefore, Uncommon term = LCMHCF = x4−1x2−1 = x2 + 1

If the HCF and the LCM of the polynomial are $x^{2}$ - 1, $x^{4}$ - 1 respectively. Find out the uncommon factor of the two polynomials.

The correct option is D
$x^{2}$ + 1

LCM = HCF $\times$ Uncommon terms

Then by dividing a LCM by HCF of polynomials we get the required uncommon term.

Therefore, Uncommon term = $\frac{L C M}{H C F}$ = $\frac{x^{4} - 1}{x^{2} - 1}$ = $x^{2}$ + 1