Question

How do you factor the trinomial `P^2-16p+64`?

Answer 1

Graph it, or use the quadratic formula `x=(-b±sqrt(b^2-4ac))/(2a)`, for `ax^2+bx+c` , or use inspection.

Explanation:

Inspection will always be the fastest, but if you're stuck, or just want to be accurate, those other methods will do.

Graphing:

`y=x^2-16x+64`
graph{x^2-16x+64 [-4.66, 20.64, -6.33, 6.33]}.
The only x-intercept is at (8,0) so we know that the only factor of this is `(x-8)^2`.

Inspection:

Make two binomials`(x+?)(x+?)`

The sum of the two unknown values must be equal to -16, and the product of the two values must be 64. Therefore, the only number that satisfies these conditions is -8. Therefore the factors of the quadratic expression are `(x-8)(x-8)`.

The quadratic formula:

I posted it in the answer section. In this case,
`a=1,b=-16`, and `c=64`
Then, substitute the variables in the quadratic formula for their respective values and your calculator will spit out an answer.