Factoring trinomials

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Jennifer3

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Oct 27, 2005
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We did this at the beginning of the year but my teacher's making us review it and I completly forgot how to do this

4t squared+12t+9 Is this a trinomial square?

Also when I factor this would I put in a 4 or 2 because 2 is the square root of 4? I'm guessing 2 because another problem is 81x squared-18x+1 and I'd think they'd want us to use 9 instead of 81
 
Jennifer3 said:
We did this at the beginning of the year but my teacher's making us review it and I completly forgot how to do this

4t squared+12t+9 Is this a trinomial square?

Also when I factor this would I put in a 4 or 2 because 2 is the square root of 4? I'm guessing 2 because another problem is 81x squared-18x+1 and I'd think they'd want us to use 9 instead of 81
Click to expand...

If it is a perfect square, that is (at + b)^2, then it should look like this:
(at + b)(at + b) = a^2t^2 + 2atb + b^2

Compare this to your expression:
4t^2 + 12t + 9
(2t)^2 + 2*(2t)* 3 + 3^2

Do you see that you can write this as
(2t + 3)(2t + 3)

Use FOIL multiplication to check:
2t*2t + 2t*3 + 3*2t + 3*3
4t^2 + 6t + 6t + 9
4t^2 + 12t + 9

This is the expression you started with. So, the factorization of 4t^2 + 12t + 9 is
(2t + 3)^2

I hope this helps you.
 
Thank you! The reason I couldn't get it to work was I didn't put 2t in both of the parentheses
 
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