Question

Factor the trinomial 2x^2 + 17x - 9 on your paper. Which of the following would be part of the factored answer?

(2x + 1)
(2x - 1)
(x - 9)
none of the above

Answer 1

(2x-1)(x+9)= 2x2 +18x -x -9
- so from this result that 2x-1 can being from what you have wrote there

Answer 2

This may be a bit exhaustive, but let me know if it helps.

When the coefficient of x^2 is not one, then you must multiple the first and last numbers together (-18).

Once you have this number, you need to find two factors of the new number (-18) whose difference (or sum) equals the middle number (+17).

In this case, +18 plus -1 equals +17. So the middle term (+17x) needs to be split up into two new terms (+18x) and (-1x).

Once you have these split up, then you can begin factor by grouping.

Factor by Grouping: 2x^2+18x-1x-9
Take the first two terms and find the Greatest Common Factor (GCF). It is 2x. Factor this value out. 2x(x+9)

Now take the second two terms and factor out the GCF. -1(x+9)

Now the expression looks like 2x(x+9)-1(x+9).
In each product there is an (x+9) in common that can also be factored out, leaving the 2x and the -1.

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