Question

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

Answer 1

See below:

Explanation:

`y=n^2-16n+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:

`(n+x)(n+y)`

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:
`(n-8)(n-8)`

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]}