Question

vü)2r? - 3x? - 9x + 5, 2x4 – x? - 10.x² – 11x + 8 whose GCD is 2x - 1
Find the GCD of each pair of the following polynomials​

Answer 1

Answer:

We know that if p(x) and q(x) are two polynomials, then p(x)×q(x)= {GCD of p(x) and q(x)}× {LCM of p(x) and q(x)}.

Now, it is given that the GCD of the polynomials 2x

3

−3x

2

−9x+5 and 2x

4

−x

3

−10x

2

−11x+8 is (2x−1), therefore, we have:

(2x

3

−3x

2

−9x+5)(2x

4

−x

3

−10x

2

−11x+8)=(2x−1)×LCM

⇒LCM=

(2x−1)

(2x

3

−3x

2

−9x+5)(2x

4

−x

3

−10x

2

−11x+8)

To find the LCM, we have to do the long division as shown in the above image:

On dividing 2x

4

−x

3

−10x

2

−11x+8 by (2x−1), the quotient is x

3

−5x−8 and the remainder is 0, therefore,

LCM=(2x

2

+x−5)(x

3

+8x

2

+4x−21)

Hence, the LCM of 2x

3

−3x

2

−9x+5 and 2x

4

−x

3

−10x

2

−11x+8 is (2x

2

+x−5)(x

3

+8x

2

+4x−21).

Answer 2

Answer:

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