Answer:
(2x + 1)(x + 4)
Explanation:
2x² + 9x + 4 cannot be factored normally - we must use the grouping technique (a > 1).
First, check for a GCF. Because there is not a GCF within this (factors of 9 are 1 and 3 - taking a 1 out is pointless), we will instead break the equation into two factors.
2x² will be apart of the first factor. You want to break the 9x into factors that will evenly break down with the 2x^2, so 3x will not work.
Your grouping factors should then be (2x^2 + 8x)(x + 4).
Then, take out the GCFs of the factors.
2x can come out of (2x^2 + 8x), so your new factor is 2x(x + 4). Your second factor set has no GCF, so you take out a 1 and get 1(x+4). In order to verify you did this correctly, the terms having the GCF distributed cannot be different in anyway.
Your factors are now (2x + 1)(x + 4) take the two GCFs and make them a factor set, then the second factor is the common factor.