# Factoring Trinomials

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• Apr 24th 2012, 07:54 PM
Kibbygirl
Factoring Trinomials
My problem states to factor completely:

49c+56c+16

Nothing can be factored out as it is. So I took the product of 49 & 16 = 784 and two integers whose products equal 784 and sum equals 56 is (28)(28)

Yet when I go to factor, it's not adding up. Maybe I am confusing the steps?

49c2+28c+28c+16

28c(c+21c) ?

I am not sure what I am suppose to do actually...
• Apr 24th 2012, 08:13 PM
princeps
Re: Factoring Trinomials
• Apr 24th 2012, 08:13 PM
highvoltage
Re: Factoring Trinomials
• Apr 24th 2012, 08:20 PM
Soroban
Re: Factoring Trinomials
Hello, Kibbygirl!

Quote:

Factor completely: . $49c^2+56c+16$

Nothing can be factored out as it is.
So I took the product of 49 & 16 = 784
. . and two integers whose products equal 784 and sum equals 56 is (28)(28).

Yet when I go to factor, it's not adding up. Maybe I am confusing the steps?

$49c^2+28c+28c+16$ . This is correct!

28c(c+21c) ? .But what is this?

You are supposed to "factor by grouping".
Are you familiar with it?

You have: . $49c^2 + 28c + 28c + 16$

Factor the terms "by pairs".
. . You can factor $7c$ from the first two terms
. . You can factor $4$ from the last two terms.

Then you have: . $7c(7c+4) + 4(7c+4)$

Note that the term groups have $(7c+4)$ on common . . . factor it out!

And we have: . $(7c+4)(7c+4) \:=\:(7c-4)^2$

See how it works?

• Apr 24th 2012, 09:58 PM
Kibbygirl
Re: Factoring Trinomials
Thank you! I didn't realize I should be factor by grouping, I was trying to do the form x2+bx+c. I am vaguely familiar with factoring by grouping, so thank you for the steps.
• Apr 25th 2012, 07:15 AM
Kibbygirl
Re: Factoring Trinomials
Soroban, can you tell me why in your final it is - and not +? Everything I am seeing in my book shows it'd be (7c+4)2??
• Apr 25th 2012, 07:16 AM
a tutor
Re: Factoring Trinomials
Quote:

Originally Posted by Kibbygirl
Soroban, can you tell me why in your final it is - and not +? Everything I am seeing in my book shows it'd be (7c+4)2??

That was just a typo.
• Apr 25th 2012, 08:04 AM
Kibbygirl
Re: Factoring Trinomials
Ok great, just wanted to verify in case I am not understanding correctly. :)