Posted by Mallory on Wednesday, February 29, 2012 at 8:04am.
Can someone please tell me Why is (4x + 5) (2x  1) + (x  9) (2x  1) not in factored form? What is the correct final factored form? What is this factoring method called?

Math  MathMate, Wednesday, February 29, 2012 at 9:14am
If it is in factored form, it should have a common factor for the whole expression.
(4x+5) is not a factor for the whole expression, just the first term (before the + sign).
To factor "completely", we need to expand the expression, collect similar terms and factor from there.
(4x + 5) (2x  1) + (x  9) (2x  1)
=8x²+6x5 + 2x²19x+9
=10x²13x+4
=(5x4)(2x1) 
Math  Steve, Wednesday, February 29, 2012 at 10:57am
Or, note that (2x1) is a common factor, so if you factor it out, you get
(2x1)(4x+5 + x9) = (2x1)(5x4) 
Math  MathMate, Wednesday, February 29, 2012 at 3:26pm
Thanks, Steve!