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

1 Answer
Apr 26, 2018

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.