Question

(b^2-10b+21)/(b^2-11b+28)

I need help trying to figure out how to factor each quantity or parentheses.

and then simplifying it.

Answer 1

For (b^2-10b+21), start with listing the factors that multiply to give 21.
1,21
3,7
7,3
21,1
As 21 is positive and -10b is negative, you will find that the factors are in the following form:
(b-x)(b-y)
where x and y are chosen from the pair of factors. If you multiply out the factors, you will get
(b-x)(b-y)=b^2-(x+y)b+xy
Thus, you will choose from the list of factors a pair which will give
xy=21 and x+y=10.
Try the same for the denominator. It has more factors, so the list of factors will look like:
1,28
2,14
4,7
7,4
14,2
28,1
The method to follow is exactly the same as the numerator.
Tell us what you found.