Find the L.C.M. of the polynomials (x+3)(-6x^ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $p(x) = (x+3)(-6x^2+5x+4)$.Factorizing the quadratic expression: $-6x^2+5x+4 = -6x^2+8x-3x+4 = -2x(3x-4)-1(3x-4) = -(3x-4)(2x+1)$.So,$p(x) = -

Vedclass · Accepted Answer

$-(x+3)^2(3x-4)(2x+1)$

Vedclass · Answer

(A) Let $p(x) = (x+3)(-6x^2+5x+4)$.Factorizing the quadratic expression: $-6x^2+5x+4 = -6x^2+8x-3x+4 = -2x(3x-4)-1(3x-4) = -(3x-4)(2x+1)$.So,$p(x) = -(x+3)(3x-4)(2x+1)$.Let $q(x) = (2x^2+7x+3)(x+3)$.Factorizing the quadratic expression: $2x^2+7x+3 = 2x^2+6x+x+3 = 2x(x+3)+1(x+3) = (2x+1)(x+3)$.So,$q(x) = (2x+1)(x+3)(x+3) = (x+3)^2(2x+1)$.The $L.C.M.$ is the product of the highest powers of all prime factors present in the expressions.$L.C.M. = -(x+3)^2(3x-4)(2x+1)$.

Find the $L.C.M.$ of the polynomials $(x+3)(-6x^2+5x+4)$ and $(2x^2+7x+3)(x+3)$.

Similar Questions

Find the $L.C.M.$ of the polynomials $30 x^{2}+13 x-3$ and $25 x^{2}-30 x+9$.

The $H.C.F.$ of $(2x^2 - 4x)$,$(3x^4 - 12x^2)$,and $(2x^5 - 2x^4 - 4x^3)$ is

The $L.C.M.$ and $H.C.F.$ of two polynomials $p(x)$ and $q(x)$ are $36 x^{3}(x+a)(x^{3}-a^{3})$ and $x^{2}(x-a)$ respectively. If $p(x)=4 x^{2}(x^{2}-a^{2})$,find $q(x)$.

Find the $G.C.D.$ of $8(x^{4}-16)$ and $12(x^{3}-8)$.

Find the $G.C.D.$ of $8(x^{3}-x^{2}+x)$ and $28(x^{3}+1)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module