I need help with Algebra (Factoring Trinomials)?

Okayyy. First, in factoring you approach the problem first with determining any least common factors. In 4v^2-22b+10 you have a least common factor of 2. If you factor out the 2 out of the entire trinomial, you get 2(2b^2-11b+5). (This is true because if you distribute the two into the parentheses you get 4b^2-22b+10). Now that you have this, you will focus on what's on the INSIDE of the parenthesis to factor further. There are several ways of approaching this, but this is how I would do it: The first terms inside the parentheses must have the variable, b, in it. You have to find two factors, that both have the variable, b, that will give you 2b^2. The only possibilities in this case are 2b and b. Therefore, you can conclude this: 2(2b ___)(b ____). Then, you have to find two numbers that, when one is multiplied by 2b, and the other by b (because these are the two factors you have as your first terms in the parentheses), you get -11b. By guess and check, you find that 5 and 1 are your two digits--5 times 2b is 10b. 1 times b is 1b. 10b + 1b is 11b...To get -11b you simply make 5 and 1 both negative. You will place these numbers in the set of parentheses OPPOSITE of the term you are multiplying them by. To get -11b, you multiply -5 by 2b, so -5 will go in the set of parentheses that does not have 2b. Same goes for -1b. Now you have 2(2b - 1)(b - 5). Tada!

Reference: my knowledge