Find the HCF of the following polynomials- P x -8 x 4-16Q x -12 x 3-8A- 4x-2B- 12 x -2C- x-2x2-2 x-4D- x 2-4

The correct option is A 4(x 2)P(x) = 8(x^4 16) = 2^3(x^2 4)(x^2+4) = 2^3(x 2)(x+2)(x^2+4) Q(x) =12(x^3 8) = 2^2× 3× (x 2)(x^2+2x+4) The common irreducible fac ...

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Byju's Answer

Standard X

Mathematics

Division Algorithm for a Polynomial

Find the HCF ...

Question

Find the HCF of the following polynomials.
P(x) = 8 $(x^{4} - 16)$
Q(x) = 12 $(x^{3} - 8)$

4 (x - 2)

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(x - 2)

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

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(x^{2} + 4)

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Solution

The correct option is A $4 (x - 2)$
P(x) = $8 (x^{4} - 16) = 2^{3} (x^{2} - 4) (x^{2} + 4) = 2^{3} (x - 2) (x + 2) (x^{2} + 4)$
Q(x) = $12 (x^{3} - 8) = 2^{2} \times 3 \times (x - 2) (x^{2} + 2 x + 4)$

The common irreducible factors of P(x) and Q(x) are 2 and (x-2)
The smallest exponents of these factors in P(x) and Q(x) are 2 and 1 respectively.

Hence, the HCF = $2^{2} \times (x - 2) = 4 (x - 2)$ .

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Similar questions

Subtract: 2 x^{2} + 6 - 4 x from 3 x^{2} - 6 x + 8.

Q. For what values of

a

and

b

the polynomials

p (x) = (x^{2} + 5 x + 6) (x^{2} + 2 x - a)

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q (x) = (x^{2} - x - 2) (x^{2} + 7 x + b)

have

(x + 2) (x - 2)

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Q. For what values of

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and

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p (x) = (x^{2} + 3 x + 2) (x^{2} + 2 x + a)

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q (x) = (x^{2} + 7 x + 12) (x^{2} + 7 x + b)

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(x + 3) (x + 4)

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Q. Question 30

The value of

(2 x^{2} + 4) \div 2

is
a)

2 x^{2} + 2

x^{2} + 2

x^{2} + 4

2 x^{2} + 4

Q. Subtracting

2 x^{2} + 6 - 4 x

from

3 x^{2} - 6 x + 8

gives .

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Find the HCF of the following polynomials. P(x) = 8(x4−16) Q(x) = 12(x3−8)

Find the HCF of the following polynomials.
P(x) = 8 $(x^{4} - 16)$
Q(x) = 12 $(x^{3} - 8)$