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

Apr 26, 2018

Graph it, or use the quadratic formula x=(-b±sqrt(b^2-4ac))/(2a), for $a {x}^{2} + b x + c$ , 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:

$y = {x}^{2} - 16 x + 64$
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 ${\left(x - 8\right)}^{2}$.

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 $\left(x - 8\right) \left(x - 8\right)$.

$a = 1 , b = - 16$, and $c = 64$