Question

Solve the quadratic equation y2 - 5y = -4 by factoring.

Answer 1

y^2 - 5y + 4 = 0

when factoring in the form (x + a)(x + b)

you know it'll be x^2 + ax + bx + ab

so you want:
ab = 4
and
ax + bx = -5x -- which is (a + b) = -5

[CAN BE SOLVED BY SUBSTITUTION (lmk if you want details on that) OR CAN BE SOLVED BY TRIAL AND ERROR/LOGIC]

I'll show you the logic since substitution sometimes takes longer and mental math is awesome :) :

so to have ab = 4 your options are either a and b are both 2, or one of them is 4 and one of them is 1. (note since +4, either both positive or both negative)

to have it correspond with a + b = - 5 . as you can see, a and b are -4 and -1 (in any order in this case; rarely the case)

so factoring is (x - 1)(x - 4)