Question

When using the inspection method to rewrite the rational expression x2−10x+14x−8, what constant term must the numerator have for (x−8) to be one of its factors? What number must you add to (and subtract from) the numerator's constant term to derive (x−8) as a factor?

Answer 1

using remainder's theorem you'll have
\[x^2 - 10x +14x - 8 + k = 0\]
since you want x-8 to be its factor
then you'll have the value of x as
x - 8 = 0
x = 8
plugging it in to the equation
\[8^2 - 10(8) +14(8) - 8 + k = 0\]
\[k + 88 = 0\]
\[k = -88\]

Answer 2

so show me how you got to k=88=0