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

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

Question

(B) Let $p(x) = x^{2}-4$.Using the identity $a^{2}-b^{2} = (a-b)(a+b)$,we get:$p(x) = (x-2)(x+2)$.Now,let $q(x) = x^{2}-5x+6$.To factorize this quadra

Vedclass · Accepted Answer

$x-2$

Vedclass · Answer

(B) Let $p(x) = x^{2}-4$.Using the identity $a^{2}-b^{2} = (a-b)(a+b)$,we get:$p(x) = (x-2)(x+2)$.Now,let $q(x) = x^{2}-5x+6$.To factorize this quadratic,we look for two numbers whose product is $6$ and sum is $-5$. These numbers are $-2$ and $-3$.$q(x) = x^{2}-2x-3x+6$$q(x) = x(x-2)-3(x-2)$$q(x) = (x-2)(x-3)$.The $G.C.D.$ (Greatest Common Divisor) is the highest degree common factor present in both polynomials.Comparing $p(x) = (x-2)(x+2)$ and $q(x) = (x-2)(x-3)$,the common factor is $(x-2)$.Therefore,the $G.C.D.$ is $x-2$.

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

Similar Questions

The $H.C.F.$ (Highest Common Factor) of two polynomials is $(y-7)$ and their $L.C.M.$ is $y^{3}-10y^{2}+11y+70$. If one of the polynomials is $y^{2}-5y-14$,find the other.

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

The $L.C.M.$ of $(x^{2}-y^{2})$,$(x^{3}-y^{3})$,and $(x^{3}-x^{2}y-xy^{2}+y^{3})$ is

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

Find the $G.C.D.$ of the polynomials $6 x^{2}+11 x+3$ and $2 x^{2}+x-3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module