Question

Find the LCM and the HCF of the polynomials (x² - 1) (x² + x - 2) and (x² + 2x + 1) (x² + 2x - 3).
Verify if the product of the LCM and the HCF is equal to the product of polynomials.

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Answer 1

Answer:

lcm=(x+1)^2(x-1)^2(x+2)(x+3)

hcf=(x+1)(x-1)

Step-by-step explanation:

(x^2-1)(x^2+x-2)=(x+1)(x-1)(x+2)(x-1)  [x^2+x-2=x^2+2x-x-2]

x^2+2x+1)(x^2+2x-3)=(x+1)^2(x+3)(x-1)

lcm=(x+1)^2(x-1)^2(x+2)(x+3)

hcf=(x+1)(x-1)

lcm*hcf=x+1)^3(x-1)^3(x+2)(x+3)=product of the given numbers