Answer :
Answer:
(z-10)²
Step-by-step explanation:
There are multiple ways of factorisation for ax²+bx+c. The easiest here is by finding 2 numbers (let's say a and b) that multiply to get c (in this case, 100), and add to get b (in this case, -20). This gives a result of (x+a)(x+b). This method only works when a=1 (which is true in this case).
For z²-20z+100, the z is the same as the x above is.
Since we are looking for 2 numbers to multiply to a positive, the 2 values must both be positive or both be negative. Adding 2 positives gives a positive result, which doesn't work here, so we must use 2 negatives.
From here, it's just a case of trial and error through the negative factor pairs of 100 (-1 and -100, -2 and -50, -4 and -25, -5 and -20, -10 and -10).
The only result here that adds to give -20 is -10 and -10.
This can be placed in the factorised form of (z-10)(z-10), as described above.
Since both brackets are the same, it can be simplified to (z-10)².
**You may want to revise factorising monic quadratics, and then move on to non-monic ones. I'm always happy to help!