Question

24) Find the LCM of (2x3° x 5
(2*3' x 54), (22x3x52x7)​

Answer 1

Answer:

Gini Uni

Step-by-step explanation:

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

+15x

2

+2x−35 and x

3

+8x

2

+4x−21 is (x+7), therefore, we have:

(2x

3

+15x

2

+2x−35)(x

3

+8x

2

+4x−21)=(x+7)×LCM

⇒LCM=

(x+7)

(2x

3

+15x

2

+2x−35)(x

3

+8x

2

+4x−21)

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

On dividing 2x

3

+15x

2

+2x−35 by (x+7), the quotient is 2x

2

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

LCM=(2x

2

+x−5)(x

3

+8x

2

+4x−21)

Hence, the LCM of 2x

3

+15x

2

+2x−35 and x

3

+8x

2

+4x−21 is (2x

2

+x−5)(x

3

+8x

2

+4x−21).

solution