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  4. The HCF and LCM of the polynomials p(x) and q(x) are 5(x-2)(x+9) and 10(x2+16 x+63)(x-2)2. If p(x) is 10(x+9)(x2+5 x-14), then q(x) is

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Q. The HCF and LCM of the polynomials $p(x)$ and $q(x)$ are $5(x-2)(x+9)$ and $10\left(x^2+16 x+63\right)(x-2)^2$. If $p(x)$ is $10(x+9)\left(x^2+5 x-14\right)$, then $q(x)$ is

Polynomials

Solution:

(i) $p(x) q(x)= LCM \times$ HCF
(ii) $LCM \times HCF = \pm f(x) \times g(x)$.
(iii) $x^2+16 x+63=(x+7)(x+9)$
$x^2+5 x-14=(x+7)(x-2)$.