If (x-a) is the G.C.D. of x^{2}-x-6 and x^{2} | vedclass

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(A) Let $p(x) = x^{2}-x-6$ and $q(x) = x^{2}+3x-18$.Since $(x-a)$ is the $G.C.D.$ of $p(x)$ and $q(x)$,$(x-a)$ must be a common factor of both polynom

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Let $p(x) = x^{2}-x-6$ and $q(x) = x^{2}+3x-18$.Since $(x-a)$ is the $G.C.D.$ of $p(x)$ and $q(x)$,$(x-a)$ must be a common factor of both polynomials.Factorizing $p(x)$:$p(x) = x^{2}-3x+2x-6 = x(x-3)+2(x-3) = (x-3)(x+2)$.Factorizing $q(x)$:$q(x) = x^{2}+6x-3x-18 = x(x+6)-3(x+6) = (x-3)(x+6)$.The common factor is $(x-3)$.Comparing $(x-3)$ with $(x-a)$,we get $a = 3$.

If $(x-a)$ is the $G.C.D.$ of $x^{2}-x-6$ and $x^{2}+3x-18$,find the value of $a$.

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