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