Question

Factor the polynomial: 32a^2b^2+16ab^2+2b^2

Answer 1

\(32a^2b^2+16ab^2+2b^2\)
Start by factoring out a common term.

Answer 2

The common term would be 2 , correct?

Answer 3

That would be one factor. There is one more.

Answer 4

Like 4 too!

Answer 5

No, 4 is not common to all terms. 2 is the only constant that can be factored from all terms.

Answer 6

Okay, so after that what would be my next step?

Answer 7

2 is only part of the common factor. Have you found the rest of it?

Answer 8

Divide each term by 2 and look at what is left.

Answer 9

A and b^2

Answer 10

Ok, so divide all terms by \(b^2\) and tell me what is left.

Answer 11

Give me a sec

Answer 12

Take your time.

Answer 13

Wait you can only divide b^2 and not a!

Answer 14

One step at a time. First divide all terms by 2.
Then divide all terms by \(b^2\).
See what you have left.
And yes, it is true that you cannot divide all terms by a, but it can be factored further.

Answer 15

What do you mean by factored forward?

Answer 16

Show me what you have done. You factored out the \(2b^2\) - show me what you have left.

Answer 17

2b^2(16a+8a+1)

Answer 18

Almost.
\(2b^2(16a^2+8a+1)\)
Keep track of the exponents.

Answer 19

Factor the remaining expression just like any other quadratic expression.

Answer 20

So far I have 2b^2(4a+____)(4a+____)

Answer 21

Yes. That is exactly it.

Answer 22

The last numbers in each factor must multiply to be +1. What are the factors of 1?

Answer 23

1 (:

Answer 24

Thank you so much for the help(: I appreciate it so much (:

Answer 25

Your welcome.