Question 490772
Factor 4x^2 – 14x – 8

There are no numbers whose sum is -14 and can multiple to make 4... I feel like I'm missing something?


Yes, you are missing something. The sum needs to be - 14, but the product is not 4, but - 32 (c * a, or - 8 * + 4) instead. However, before you factor this trinomial, you would need to first find and use its GCF, as follows:


{{{2(2x^2 - 7x - 4)}}}


Now, as you can see, we have to find two factors whose sum is - 7, and whose product is - 8 (c * a, or - 4 * + 2). These two factors are: - 8 and + 1


We now have: {{{2(2x^2 - 8x + x - 4)}}} ----- 2[2x(x - 4) + 1(x - 4)] ---- {{{highlight_green(2(2x + 1)(x - 4))}}}