Question

Find the HCF and LCM of the following f(x)=2x²-5x²=3x and g(x)=x⁴-27x

Answer 1

Answer:

Let f(x)=x

4

+3x

3

+5x

2

+26x and g(x)=x

4

+2x

3

−4x

2

−x+28

Given that GCD =x

2

+5x+7. Also, we have GCD × LCM= f(x) × g(x).

Thus, LCM=

GCD

f(x)×g(x)

Now, GCD divides both f(x) and g(x).

Let us divided f(X) by the GCD.

When f(x) is divided by GCD, we get the quoteint as x

2

−2x+8.

Now, (1) → LCM =(x

2

−2x+8)×g(x)

Thus, LCM =(x

2

−2x+8)(x

4

+2x

3

−4x

2

−x+28).