Question

The H.C.F. of two polynomials is (x - 1) (x + 2) and their L.C.M. is $x^2-2x-3$. If one of the polynomials is $x^2+x-2$, find the other polynomial.

• A. $x^2-x+3$
• B. $x^2+2x+3$
• C. $2x^2-2x+3$
• D. $x^2-2x+3$

Answer 1

The correct option is D $x^2-2x+3$

Let f(x) = $x^2+x-2$
$x^2+2x-x-2$ = x (x + 2) -1 (x + 2)
$=(x-1)(x+2)$

L.C.M. = $x^2-2x+3$
$x^2-2x-3$ = $x^2+x-3x-3$
$=(x+1)(x-3)$

Let the other polynomial be g(x),
$f\left(x\right)\times g\left(x\right)=H.C.F.\times L.C.M.$

So, $g\left(x\right)=\frac{H.C.F.\times L.C.M}{f\left(x\right)}$
$g\left(x\right)=\frac{(x-1)(x+2)\times (x+1)(x-3)}{(x-1)(x+2)}$

$g\left(x\right)=x^2-2x+3$

Thus the correct option is D.