Question

how to find hcf and lcm of polynomials

Answer 1

Hello User!!!!!


I will give you an example by way of a problem.

Problem: Find the HCF, h(x) and LCM, m(x) of the polynomials p(x) = 2x^2 + 7x + 5 and q(x) = 8x^3 + 125. Is it true p(x).q(x) = h(x).m(x)?

Solution: we have p(x) = 2x^2 + 7x + 5 = (2x+5)(x+1) … (1)

q(x) = 8x^3 + 125 = (2x+5)(4x^2–10x+25) … (2)

Hence h(x) = (2x+5) … (3) and

m(x) = (2x+5)(x+1)(4x^2–10x+25) … (4)

Next p(x).q(x) = (2x+5)(x+1)(2x+5)(4x^2–10x+25) =(2x+5)^2(x+1)(4x^2–10x+25) …(5)

h(x).m(x) = (2x+5)(2x+5)(x+1)(4x^2–10x+25)= (2x+5)^2(x+1)(4x^2–10x+25) … (6)

We can see from (5) and (6) that p(x).q(x) = h(x).m(x).


Hope it helps you.

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