Question

$x^2 - 5x + 6$ factor completely; $x(x - 10)$; $(x - 3)(x - 2)$; $(x + 3)(x - 2)$; $(x - 3)(x + 2)$

Explanation:

Step1: Identify $a,b,c$ for $ax^2+bx+c$

For $x^2 - 5x + 6$, $a=1$, $b=-5$, $c=6$

Step2: Find pair with sum $b$, product $ac$

Need two numbers: sum $=-5$, product $=1\times6=6$. The numbers are $-3$ and $-2$.

Step3: Split middle term and factor

$$\begin{align*} x^2 - 5x + 6&=x^2 -3x -2x +6\\ &=x(x-3)-2(x-3)\\ &=(x-3)(x-2) \end{align*}$$

Answer:

B. $(x - 3)(x - 2)$