Question

If the HCF of \(x^2 - x - 6\) and \(x^2 + 9x + 14\) is (x + m), then the value of m is:

(a) 1

(b) 2

(c) –2

(d) –1

Answer 1

Correct option : (b) 2

\(x^2 - x - 6 = x^2 -3x + 2x-6 =x(x-3)+ 2(x-3)\)

\(=(x-3)(x+2)\)

\(x^2 + 9x + 14 =x^2 +2x +7x +14\)

\(=x(x+2)+7(x+2) = (x+2)(x+7)\)

\(\therefore \) HCF of \(x^2 - x - 6\) and \(x^2 + 9x + 14\) is (x + 2)

\(\therefore m=2.\)