What is the H-C-F of x 2-2 x -8- x 3-4 x 2-4 x - x 2-4A- x -2B- x -1C- x-3 D- X 2

The correct option is A x 2 Factors of : x^2+2x 8 → (x+4)(x 2) x^3 4x^2+4x → x (x 2)^2 x^2 4 → (x+2)(x 2) The highest common factor for the above expressions ...

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Standard X

Mathematics

GCD of Polynomials

What is the H...

Question

What is the H.C.F of $x^{2} + 2 x - 8, x^{3} - 4 x^{2} + 4 x, x^{2} - 4$

$x - 2$

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$x + 3$

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$x^{2}$

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$x + 1$

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Solution

The correct option is A
$x - 2$

Factors of :
$x^{2} + 2 x - 8 \to (x + 4) (x - 2)$

$x^{3} - 4 x^{2} + 4 x \to x (x - 2)^{2}$

$x^{2} - 4 \to (x + 2) (x - 2)$

The highest common factor for the above expressions is $(x - 2)$
$∴$ H.C.F = $(x - 2)$

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Similar questions

Q. The H.C.F. of

x^{2} + 2 x - 8, x^{3} - 4 x^{2} + 4 x

and

x^{2} - 4

is .

Q. Find the limits :

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

Q. What is the quotient obtained when

x^{3} + x^{2} - 5 x + 3

is divided by

x^{2} + 2 x - 3

Q. Find the H.C.F. of

(x^{2} + x + 1)

and

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

by using the division method.

\frac{x^{2} - 7 x + 10}{x^{2} - 5 x - 14} \times \frac{x^{3} + 8}{x^{3} - 8} \times \frac{x^{2} + 2 x + 4}{x^{2} - 2 x + 4} \times \frac{x - 7}{x - 5} = ?

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What is the H.C.F of x2+2x−8,x3−4x2+4x,x2−4

The correct option is A x−2 Factors of : x2+2x−8→(x+4)(x−2) x3−4x2+4x→x(x−2)2 x2−4→(x+2)(x−2) The highest common factor for the above expressions is (x−2) ∴ H.C.F = (x−2)

What is the H.C.F of $x^{2} + 2 x - 8, x^{3} - 4 x^{2} + 4 x, x^{2} - 4$

The correct option is A
$x - 2$

Factors of :
$x^{2} + 2 x - 8 \to (x + 4) (x - 2)$

$x^{3} - 4 x^{2} + 4 x \to x (x - 2)^{2}$

$x^{2} - 4 \to (x + 2) (x - 2)$

The highest common factor for the above expressions is $(x - 2)$
$∴$ H.C.F = $(x - 2)$