Pls help!
Factor: z^2 -20z + 100

(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!