f(x), g(x) are two polynomial with integer co-efficient such that their H.C.F. is 1
and L.C.M. is (x2
-4) (x4 – 1). If f(x) = x3– 2x2 – x + 2 then g(x) is.
Answers
Answered by
2
Answer:
Step-by-step explanation:
ANSWER
HCF×LCM=f(x)×g(x)
g(x)=
x
3
−2x
2
−x+2
1×(x
2
−4)(x
4
−1)
,f(x)=x
3
−2x
2
−x+2; (x−1) is a factor of f(x),
∴x
3
−2x
2
−x+2
=x
2
(x−1)−x(x−1)−2(x−1)
=(x−1)(x
2
−x−2)
=(x−1)(x−2)(x+1)
∴g(x)=
(x−1)(x−2)(x+1)
(x−2)(x+2)(x+1)(x
2
+1)(x−1)
⇒g(x)=(x+2)(x
2
+1)
⇒g(x)=x
3
+2x
2
+x+2ANSWER
HCF×LCM=f(x)×g(x)
g(x)=
x
3
−2x
2
−x+2
1×(x
2
−4)(x
4
−1)
,f(x)=x
3
−2x
2
−x+2; (x−1) is a factor of f(x),
∴x
3
−2x
2
−x+2
=x
2
(x−1)−x(x−1)−2(x−1)
=(x−1)(x
2
−x−2)
=(x−1)(x−2)(x+1)
∴g(x)=
(x−1)(x−2)(x+1)
(x−2)(x+2)(x+1)(x
2
+1)(x−1)
⇒g(x)=(x+2)(x
2
+1)
⇒g(x)=x
3
+2x
2
+x+2
Similar questions