Find the G.C.D. of 3+13 x-30 x^{2} and 25 x^{ | vedclass

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

Question

(B) Let $p(x) = 3 + 13x - 30x^2$.Rearranging the terms: $p(x) = -30x^2 + 13x + 3$.Factorizing $p(x) = -30x^2 + 18x - 5x + 3 = -6x(5x - 3) - 1(5x - 3)

Vedclass · Accepted Answer

$5 x-3$

Vedclass · Answer

(B) Let $p(x) = 3 + 13x - 30x^2$.Rearranging the terms: $p(x) = -30x^2 + 13x + 3$.Factorizing $p(x) = -30x^2 + 18x - 5x + 3 = -6x(5x - 3) - 1(5x - 3) = -(6x + 1)(5x - 3)$.Let $q(x) = 25x^2 - 30x + 9$.This is a perfect square trinomial: $q(x) = (5x)^2 - 2(5x)(3) + 3^2 = (5x - 3)^2$.The $G.C.D.$ (Greatest Common Divisor) is the highest common factor between $p(x)$ and $q(x)$.Comparing $p(x) = -(6x + 1)(5x - 3)$ and $q(x) = (5x - 3)(5x - 3)$,the common factor is $(5x - 3)$.Therefore,the $G.C.D.$ is $(5x - 3)$.

Find the $G.C.D.$ of $3+13 x-30 x^{2}$ and $25 x^{2}-30 x+9$.

Similar Questions

The product of two non-zero expressions is $(x+y+z) p^{3}$. If their $H.C.F.$ is $p^{2}$,their $L.C.M.$ is

Find the $G.C.D.$ of $x^{2}-4$ and $x^{3}-5x+6$.

Find the $G.C.D.$ of the polynomials $36 x^{2}-49$ and $6 x^{2}-25 x+21$.

Find the $G.C.D.$ of the polynomials $(x-2)^{2}(x+3)(x-4)$ and $(x-2)(x+2)(x-5)$.

If $(x-4)$ is the $G.C.D.$ of $x^{2}-x-12$ and $x^{2}-mx-8$,find the value of $m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module