SOLUTION: I need and explanation for two questions I posted up for help yesterday. Answers and steps were given but the answers didn't appear to be correct: Both of these say Factor Compl

Question 173894: I need and explanation for two questions I posted up for help yesterday. Answers and steps were given but the answers didn't appear to be correct:
Both of these say Factor Completely:
12x^2 + 13x +3. The answer is (4x + 3)(3x + 1) But I do not understand we got 13 x out of 3 and 3x?? Wouldn't that be 9x??
And the second is exactly the same:
16x^4 - 40x^2 + 9. The answer was given as (4x^2 - 1)(4x^2 - 9) which can further be factored, I understand.But ok same question, since when does 1 . 4x^2 equal 40x^2? That would be 4x^2? Can someone please explain to me the step I am missing because I really feel like I am finally getting this stuff and then WHAM!!! Thanks for the help;-)
Found 2 solutions by nerdybill, solver91311:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Expand through "FOIL" (first, outer, inner and last)
.
(4x + 3)(3x + 1)
First: 4x(3x) = 12x^2
Outer: 4x(1) = 4x
Inner: 3(3x) = 9x
Last: 3(1) = 3
.
Putting it all together we have:
12x^2 + 4x + 9x + 3
12x^2 + 13x + 3
.
The second expansion works the same as above.
For review of FOIL see:
http://www.mathwarehouse.com/algebra/polynomial/foil-method-binomials.php

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Use FOIL:

First: :

Outside: :

Inside: :

Last: :

Add the first degree terms

So: and vice versa, of course.

The other problem works the same way. 4 times -9 is -36 plus -1 times 4 is -4 and -36 plus -4 is -40.
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