For two polynomial p(x) and q(x), their H.C.F. h(x) = x-2 and their L.C.M. m(x)=x2−3x+2, find the other polynomial q(x).
A
x2+x+6
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B
x2−x−6
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C
x2+x−6
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D
x2−x+6
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Solution
The correct option is Cx2+x−6 H.C.F. h(x)= (x-2) L.C.M. m(x) is x3−7x+6 =x3−1−7x+7(x3−1)−7(x−1) =(x−1)(x3+x−6)=(x−1)(x+3)(x−2) p(x)=x2−3x+2=(x−2)(x−1) Now, p(x).q(x)=h(x).m(x) ∴q(x)=h(x).m(x)p(x)=(x−2)×(x−1)(x−2)(x+3)(x−2)(x−1) =(x−2)(x+3)=x2+x−6 Thus, The other polynomial q(x)=x2+x−6