College Algebra Factoring

[Snickerdoodle]

Hi all,

I'm having trouble with this flashcard. I thought there should be 2 factored out, and it says so in the explaination, but it's not in the answer. Any help is much appreciated!

Question 1 of 1

Factor:
18x2-14x-4

Your Answer: 2(9x+2)(x-1)

Explanation

Correct Answer: (9x+1)(2x-1)

Given:
18x2-14x-4

First notice that 2 can be factored out from every term in the polynomial above.

This gives us: 2(9x2 - 7x - 2)
The inside can be factored further:
9x2 - 7x - 2 -- This is of the form:

Ax2+Bx+C


When you see this form,
Begin to factor by drawing two parentheses
( ___ _ ___ )( ___ _ ___ )

(Step 1) Determine the sign (+ or -) that goes in the middle of each parentheses.

( __ ? __ )( __ ? __ )

How?:
Look at the last sign:
9x2 - 7x - 2

if the last sign is (-), as it is here, then the signs alternate: ( __ - __ )( __ + __ )

NOTICE:If it is (+), the two signs will be the same.
Either ( __ + __ )( __ + __ ) or ( __ - __ )( __ - __ ).

(Step 2) Next determine the first and last numbers for each parentheses.

( ? - ? )( ? + ? )

How?
List the factors of the first and last terms:
9x2 - 7x - 2

Since the last sign, as we determined above, is (-), the signs are different in either parentheses
and therefore the factors in the above table must SUBTRACT to the middle term of 14x.

And since 9x - 2x = 7x, we have picked the correct factors of the first and last terms.

The factors of the first and last terms are arranged in the parentheses in this way every time:
( # +/- # )( # +/- # )

Now look to see if there is a (+) or (-) sign in the middle:
9x2 - 7x - 2

The middle term is (-), and since the A term is 18, we need to perform a "check"
before we know where to place the (-) sign.

If we place the (-) sign in the first parentheses:
(9x-1)(2x+1)
Then Check:

(1) Multiply the inner terms: -1 * 2x = -2x

(2) Multiply the outer terms: 9x * (+1) = 9x

Then add -2x+9x = +7x
* Therefore this is wrong; our middle term is NOT (+)

If we place the (-) sign in the second parentheses:
(9x+1)(2x-1)
Then Check:

(1)Multiply the inner terms:+1 * (2x) = +2x

(2) Multiply the outer terms:9x * (-12) = -9x

Then add +2x-9x = -7x
* This IS our middle term, therefore this is correct!

Therefore our solution is:
(9x+1)(2x-1), which can also be written (2x-1)(9x+1).