How do you factor y=n^2-16n+64 ?

Apr 11, 2018

See below:

Explanation:

$y = {n}^{2} - 16 n + 64$

I think the easiest way to think about a problem when asked to factorize is: "What two numbers, when added gives -16, and when multiplied gives 64?"

When factoring in this case you would get:

$\left(n + x\right) \left(n + y\right)$

But we know that $x + y = - 16$ and $x \times y = 64$
And then we can conclude that the number in question must be $- 8$.

So the factorized version would be:
$\left(n - 8\right) \left(n - 8\right)$

So the quadratic has a repeated solution: $8$

$x = 8$ is therefore a solution- which can be seen in the graph of the function:
graph{x^2-16x+64 [-10, 10, -5, 5]}