How do you factor 8b ^ { 2} - 12b + 4?

2 Answers
Jul 22, 2017

Use the factors of 8b^2 and 4 to factor out the polynomial.

Explanation:

8b^2-12b+4

Since they are all factors of 4, you can easily simplify them into simpler numbers.

=4(2b^2-3b+1)

Now, just factor out the first and last term.

=(2b-1)(b-1)

Jul 22, 2017

Here's how I factor it. (Other people use different detaiols.)

Explanation:

First remove the common factor of 4

8b^2-12b+4 = 4(2b^2-3b+1)

Now we need to factor 2b^2-3b+1

Think about FOIL. If this can be factored using whole numbers we must have

F = 2b^2
O+I = -3b and
L = +1

So we start with

2b^2-3b+1 = (2b +- "something")(b +- "something")

Since L = +1 both "something"'s must be +1 or both are -1

(Or the expression cannot be factored using whole numbers.)

Try both possibilities

(2b+1)(b+1) = 2b^2 "(of course") +2b+b " STOP!" that will give us +3b -- not what we want.

Check the other possibility maybe wither one works and the expression cannot be factored using whole numbers.

(2b-1)(b-1) = 2b^2 "(of course") -2b-b +1 = 2b^2-3b+1 Good! That's it.

8b^2-12b+4 = 4(2b^2-3b+1) = 4(2b-1)(b-1)