Question

How do you factor the expression `4r^2-40r+96`?

Answer 1

`4r^2-40r+96 = 4(r-6)(r-4)`

Explanation:

Note that all of the given terms are divisible by `4`, so separate that out as a factor first then complete the square:

`4r^2-40r+96 = 4(r^2-10r+24)`

`color(white)(4r^2-40r+96) = 4(r^2-10r+25-1)`

`color(white)(4r^2-40r+96) = 4((r-5)^2-1^2)`

`color(white)(4r^2-40r+96) = 4((r-5)-1)((r-5)+1)`

`color(white)(4r^2-40r+96) = 4(r-6)(r-4)`