Question

The factorisation of $x^2-5x+6$ is

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

Answer 1

The correct option is D $(x-3)(x-2)$

The given expression is
$x^2-5x+6$
The product of first and last term is $6x^2$.
The middle term is -5x.
So, two terms whose product is $6x^2$ and sum is $-5x$ will be
$-3xand-2x$
So, the expression can be written as
$x^2-3x-2x+6$
= $x(x-3)-2(x-3)$
= $(x-3)(x-2)$ [Taking (x-3) common]