Answer:
(x+5)(x-4)(x-3)
Step-by-step explanation:
Divide (e+5) into e³-2e²-23e+60 using polynomial long division (picture attached below). Since it divides in evenly, we can see it is a factor.
So we can say e³-2e²-23e+60 = (e+5)(e²-7e+12)
To complete the factorisation, factorise e²-7e+12.
Note that (x+a)(x+b)=x²+(a+b)x+ab. So find the multiples or 12 which can be added or subtracted to get -7: -4 and -3.
e²-7e+12=(x-4)(x-3)
So e³-2e²-23e+60 = (x+5)(x-4)(x-3)
