$f (x), g (x)$ are two polynomials with integer coefficient such that their HCF is $1$ and LCM is $(x^{2} - 4) (x^{4} - 1)$ . If $f (x) = x^{3} - 2 x^{2} - x + 2$ , then $g (x)$ is

x^{3} - 2 x^{2} + x + 2

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x^{3} - 2 x^{2} + x - 2

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x^{3} + 2 x^{2} + x + 2

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x^{3} - 2 x^{2} - x - 2

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Solution

The correct option is C $x^{3} + 2 x^{2} + x + 2$
$L . C . M = \frac{f (x) . g (x)}{H . C . F}$
$∴ g (x) = \frac{(x^{2} - 4) (x^{4} - 1)}{x^{3} - 2 x^{2} - x + 2} = \frac{(x + 2) (x - 2) (x^{2} + 1) (x - 1) (x + 1)}{(x - 1) (x + 1) (x - 2)}$
$\Rightarrow x^{3} + 2 x^{2} + x + 2 = g (x)$

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Similar questions

f (x), g (x)

are two polynomial with integer coefficient such that their HCF is 1 and LCM is

(x^{2} - 4) (x^{4} - 1)

. If

f (x) = x^{3} - 2 x^{2} - x + 2

, then

g (x)

f (x), g (x)

are two polynomial with integer coefficient such that their H.C.F. is

1

and LCM is

(x^{2} - 4) (x^{4} - 1)

. If

f (x) = x^{3} - 2 x^{2} - x + 2

, then

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$(x + 1)$ is a factor of the polynomial
(a) $x^{3} - 2 x^{2} + x + 2$ (b) $x^{3} + 2 x^{2} + x - 2$
(c) $x^{3} + 2 x^{2} - x - 2$ (d) $x^{3} + 2 x^{2} - x + 2$

If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ , divisor = $x - 1$ and remainder = 2. Find the quotient q(x)

$If the dividend = x^{4} + x^{3} - 2 x^{2} + x + 1, divisor = x - 1 and remainder = 2, then find the quotient q(x) .$

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f(x),g(x) are two polynomials with integer coefficient such that their HCF is 1 and LCM is (x2−4)(x4−1). If f(x)=x3−2x2−x+2, then g(x) is

The correct option is C x3+2x2+x+2L.C.M=f(x).g(x)H.C.F∴g(x)=(x2−4)(x4−1)x3−2x2−x+2=(x+2)(x−2)(x2+1)(x−1)(x+1)(x−1)(x+1)(x−2)⇒x3+2x2+x+2=g(x)

$f (x), g (x)$ are two polynomials with integer coefficient such that their HCF is $1$ and LCM is $(x^{2} - 4) (x^{4} - 1)$ . If $f (x) = x^{3} - 2 x^{2} - x + 2$ , then $g (x)$ is

The correct option is C $x^{3} + 2 x^{2} + x + 2$
$L . C . M = \frac{f (x) . g (x)}{H . C . F}$
$∴ g (x) = \frac{(x^{2} - 4) (x^{4} - 1)}{x^{3} - 2 x^{2} - x + 2} = \frac{(x + 2) (x - 2) (x^{2} + 1) (x - 1) (x + 1)}{(x - 1) (x + 1) (x - 2)}$
$\Rightarrow x^{3} + 2 x^{2} + x + 2 = g (x)$