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

Question

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 (A) 5(x+9)(x-2) (B) 10(x-2)2(x+7) (C) 10(x+9)(x-2) (D) 5(x-2)2(x+9)

Tardigrade Admin · Accepted Answer

(i) p(x) q(x)= LCM × HCF (ii) LCM × HCF = ± f(x) × g(x). (iii) x2+16 x+63=(x+7)(x+9) x2+5 x-14=(x+7)(x-2).

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

$5 (x + 9) (x - 2)$

$10 (x - 2)^{2} (x + 7)$

$10 (x + 9) (x - 2)$

$5 (x - 2)^{2} (x + 9)$

(i) $p (x) q (x) = L CM \times$ HCF
(ii) $L CM \times H CF = \pm f (x) \times g (x)$ .
(iii) $x^{2} + 16 x + 63 = (x + 7) (x + 9)$
$x^{2} + 5 x - 14 = (x + 7) (x - 2)$ .

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

5(x+9)(x−2)

10(x−2)2(x+7)

10(x+9)(x−2)

5(x−2)2(x+9)