17. The H.C.F and L.C.M of two expressions of the second degrees are (x-1) and (x-1) (x+1)(x+3) respectively. Find the expressions.
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0
Answer:
The GCD and LCM of two polynomials are x + 1 and x^6 - 1 respectively. If one of the polynomials is x^3 + 1 , find the other.
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Given GCD =x+1 and LCM =x
6
−1
Let f(x)=x
3
+1.
We known that LCM×GCD=f(x)×g(x)
→g(x)=
f(x)
LCM×GCD
=
x
3
+1
(x
6
−1)(x+1)
x
3
+1
(x
3
+1)(x
3
−1)(x+1)
=(x
3
−1)(x+1)
Hence, g(x)=(x
3
−1)(x+1
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