Question

find the L.C.M of the polynomial 12(x⁴-x³) and 8(x⁴-3x³+2x²)

Answer 1

Given :

• The terms $12(x^{4}-x^{3})$ and $8(x^{4}-3x^{3}+2x^{2})$

To find :

• Their LCM

Solution :

• 1st term = $12(x^{4}-x^{3})$

• $=12*x^{3}*(x-1)$

• $=2*2*3*x*x*x*(x-1)$

• 2nd term = $8(x^{4}-3x^{3}+2x^{2})$

• $=8*x^{2}*(x^{2}-3x+2)$

• $=2*2*2*x*x*(x^{2}-x-2x+2)$

• $=2*2*2*x*x*\{x(x-1)-2(x-1)\}$

• $=2*2*2*x*x*(x-1)*(x-2)$

• Thus the required LCM is

• $=2*2*2*3*x*x*x*(x-1)*(x-2)$

• $=24x^{3}(x^{2}-3x+2)$

• $=24(x^{5}-3x^{4}+2x^{3})$

Answer: LCM is $=24(x^{5}-3x^{4}+2x^{3})$

Answer 2

Answer:

f(x) = 12(x4 – x3) g(x) = 8(x4 – 3x3 + 2x2) L.C.M = 24x3 (x – 1)(x – 2) Read more on Sarthaks.com - https://www.sarthaks.com/938972/find-the-gcd-of-each-pair-of-the-following-polynomials-12-x-3-8-x-4-3x-3-2x-2-whose-lcm-is-24x-3-x-1-x