Question

The L.C.M. of two polynomials $p\left(x\right)$ and $q\left(x\right)$ is $(x+3)(x-2{)}^2(x-6)$ and their H.C.F. is $(x-2)$. If $p\left(x\right)=(x+3)(x-2{)}^2$, then $q\left(x\right)=$ ________

• A. $(x+3)(x-2)$
• B. $x^2-3x-18$
• C. $x^2-8x+12$
• D. $x^2-4x+4$

Answer 1

The correct option is C $x^2-8x+12$

As HCF is highest common factor

b/w '2' Poly.

& $\left(lcm\right)\left(hcf\right)=P\left(x\right).q\left(x\right)$

$\Rightarrow q\left(x\right)=\frac{\left(lcm\right)\left(hcf\right)}{p\left(x\right)}$

$=\frac{(x-13)(x-2)(x-6)(x-2)}{(x+3)(x-2{)}^2}$

$\Rightarrow q\left(x\right)=x^2-8x+12$