Question

the H.C.F and l.c.m of two polynomials f(x)andg(g)are x²(x-a)and26x³(x+a)(x³-a³)respectively.if f(x)=4x²(x²-a²)finel g(x)​

Answer 1

Step-by-step explanation:

Let f(x) = x

2

+x−2

x

2

+2x−x−2 = x (x + 2) -1 (x + 2)

=(x−1)(x+2)

L.C.M. = x

2

−2x+3

x

2

−2x−3 = x

2

+x−3x−3

=(x+1)(x−3)

Let the other polynomial be g(x),

f(x)×g(x)=H.C.F.×L.C.M.

So, g(x)=

f(x)

H.C.F.×L.C.M

g(x)=

(x−1)(x+2)

(x−1)(x+2)×(x+1)(x−3)

g(x)=x

2

−2x+3

Thus the correct option is D.