Question

How do you factor $x^2-45x+450$?

Answer 1

$x^2-45x+450=(x-30)(x-15)$

Explanation:

Note that $45=30+15$ and $450=30\cdot 15$

Hence:

$x^2-45x+450=(x-30)(x-15)$

Alternatively, you could find it by completing the square:

$\begin{array}{cc}4(x^2-45x+450)& =4x^2-180x+1800\\ & =(2x-45{)}^2-{45}^2+1800\\ & =(2x-45{)}^2-2025+1800\\ & =(2x-45{)}^2-225\\ & =(2x-45{)}^2-{15}^2\\ & =\left(\right(2x-45)-15)\left(\right(2x-45)+15)\\ & =(2x-60)(2x-30)\\ & =4(x-30)(x-15)\end{array}$

So dividing both ends by 4 we find:

$x^2-45x+450=(x-30)(x-15)$