Name: LCM and HCF of Algebraic Expressions
Uploaded: 2019-07-19
Duration: 11 min 33 s
Description: We all know about the LCM and HCF of numbers. Do you know about the LCM and HCF of algebraic expressions? Watch the video and find the answers to such questi...

Question

Find the L.C.M. of the following polynomials :

(x^{2} - 4) (x^{2} + 5 x + 6), {(x + 3)}^{2} (2 x^{2} + x - 6) & 4 x^{2} - 12 x + 9

Accepted Answer

Given,

$(x^{2} - 4) (x^{2} + 5 x + 6), {(x + 3)}^{2} (2 x^{2} + x - 6) & 4 x^{2} - 12 x + 9$

Prime factorize each of the given polynomials.

First polynomial $= (x^{2} - 4) (x^{2} + 5 x + 6) = (x^{2} - 2^{2}) (x^{2} + 3 x + 2 x + 6) = (x - 2) (x + 2) [x (x + 3) + 2 (x + 3)] = (x - 2) (x + 2) (x + 3) (x + 2) = (x - 2) (x + 3) {(x + 2)}^{2}$

Second polynomial $= {(x + 3)}^{2} (2 x^{2} + x - 6) = (x + 3) (x + 3) (2 x^{2} + 4 x - 3 x - 6) = (x + 3) (x + 3) (2 x (x + 2) - 3 (x + 2)) = (x + 3) (x + 3) (x + 2) (2 x - 3) = {(x + 3)}^{2} (x + 2) (2 x - 3)$

Third polynomial $= 4 x^{2} - 12 x + 9 = 4 x^{2} - 6 x - 6 x + 9 = 2 x (2 x - 3) - 3 (2 x - 3) = (2 x - 3) (2 x - 3) = {(2 x - 3)}^{2}$

Product of the L.C.M. of the leading coefficients and factors with their highest powers involved in either of the polynomials is the required L.C.M.

Hence, the required L.C.M. $= (x - 2) {(x + 3)}^{2} {(x + 2)}^{2} {(2 x - 3)}^{2}$ .

Find the L.C.M. of the following polynomials :
$(x^{2} - 4) (x^{2} + 5 x + 6), {(x + 3)}^{2} (2 x^{2} + x - 6) & 4 x^{2} - 12 x + 9$

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the L.C.M. of the following polynomials : (x2-4)(x2+5x+6), (x+3)2(2x2+x-6) & 4x2-12x+9

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the L.C.M. of the following polynomials :
$(x^{2} - 4) (x^{2} + 5 x + 6), {(x + 3)}^{2} (2 x^{2} + x - 6) & 4 x^{2} - 12 x + 9$