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GCD of Polynomials

If the HCF of...

Question

If the HCF of the polynomials $f (x)$ and $g (x)$ is $4 x - 6$ , then $f (x)$ and $g (x)$ could be :

A

2, 2 x - 3

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B

8 x - 12, 2

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C

2 {(2 x - 3)}^{2}, 4 (2 x - 3)

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D

2 (2 x + 3), 4 (2 x + 3)

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Solution

The correct option is A $2 {(2 x - 3)}^{2}, 4 (2 x - 3)$
Given, HCF $= 4 x - 6 = 2 (2 x - 3)$
Since HCF needs to be a factor of both the polynomials, clearly only option C with polynomials $2 ({2 x - 3)}^{2}, 4 (2 x - 3)$ have both factors $2$ and $(2 x - 3)$

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Similar questions

f (x) = \frac{2}{x - 3}

g (x) = \frac{x - 3}{x + 4}

h (x) = - \frac{2 (2 x + 1)}{x^{2} + x - 12}

lim x \to 3 [f (x) + g (x) + h (x)]

f (x) = \frac{2}{x - 3}, g (x) = \frac{x - 3}{x + 4}

h (x) = \frac{- 2 (2 x + 1)}{x^{2} + x - 12}

lim x \to 3 [f (x) + g (x) + h (x)]

f (x) = (x + 2) (x^{2} + 8 x + 15)

g (x) = (x + 3) (x^{2} + 9 x + 20)

then find the HCF of

f (x)

g (x)

.

f (x) = \frac{3}{x - 2} - \frac{1}{x + 3}

g (x) = \frac{x^{2} - 4 x + 19}{x^{2} + x - 6}

f (x) = g (x)

x =

Q. If the LCM of

f (x)

g (x)

6 x^{2} + 13 x + 6

and their HCF is a linear polynomial. Find the possible HCF of

f (x)

g (x)

.

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