The binomial (4x + 5) is a factor of a quadratic expression 24x^2 + 10x -25. What is the other factor of this expression?

(6x - 5)

Step-by-step explanation:

(6x - 5)(4x + 5) = 24x^2 + 10x -25

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4