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College Algebra Factoring
#1
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).
AA Liberal Studies, Thomas Edison State College-Dec. 2012
BA Liberal Studies, Thomas Edison State College-Sept. 2013
16 CLEPs, 6 DSSTs, 12 FEMAs, and a handful of B&M lab science courses
120/120 credits DONE :hurray:

“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever.”
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#2
Forgive me, but I was just thinking this. What better opportunity it is for me to CUT AND RUN! See you later and good luck!
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#3
Run, run, run away, I will find some other way. Anyone brave enough to slay this giant problem for me?
AA Liberal Studies, Thomas Edison State College-Dec. 2012
BA Liberal Studies, Thomas Edison State College-Sept. 2013
16 CLEPs, 6 DSSTs, 12 FEMAs, and a handful of B&M lab science courses
120/120 credits DONE :hurray:

“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever.”
Reply
#4
I haven't read the logic for the answer, but when I check your answer, it looks correct. It multiplies back to 18x^2-14x-4. Their answer multiplies back to 18x^2-7x-1. I think you understand how to do this one.
AS in 2010 and BS in 2013 at Excelsior College - Transcripts and Costs
MS Biostatistics in 2019 at Texas A&M University - Graduate School

Sharing Credit-by-Exam*
Resources Used - 20+ Exams Passed & General GRE
Practice Tests - Available for CLEP and DSST

* Link posted with permission from forum admin; thank you!
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#5
I looked at problem, and you got the right answer. I even double checked it with the MathWay Tool found on Free-CLEP-Prep.com and they also came up with 2(9x+2)(x-1). (MathWay Tool - Free-Clep-Prep.com)

Pretty sure they just goofed up. Esp. when it's in the explanation.
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#6
Thanks a lot guys! I just need some confirmation that I'm not seeing things like I'm crazy. Tongue Whew!
And thanks Publius for the link. It looks very useful.
AA Liberal Studies, Thomas Edison State College-Dec. 2012
BA Liberal Studies, Thomas Edison State College-Sept. 2013
16 CLEPs, 6 DSSTs, 12 FEMAs, and a handful of B&M lab science courses
120/120 credits DONE :hurray:

“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever.”
Reply


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