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?

Answer 1

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+6x-5 + 2x²-19x+9
=10x²-13x+4
=(5x-4)(2x-1)

Answer 2

Or, note that (2x-1) is a common factor, so if you factor it out, you get

(2x-1)(4x+5 + x-9) = (2x-1)(5x-4)

Answer 3

Thanks, Steve!