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# This is very stupid.

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This could technically be classified as off topic but it does have to do with math.

In any math book I work in, I figure out the answer and put it down, but the book always has a different answer, even if the two equations have the same graph! I am in algebra II and this book is driving me INSAAAAANE!

an example of this is shown here:

"Write the expression in factored form: 16-2x^2

I found (4+sqrt(2)x)(4-sqrt(2)x)

The book, however, decided the correct answer was -2(x^2-8)

Don't believe those give the same graph? Go here! https://www.desmos.com/calculator

Enter those three equations and you will see the results.

How do I turn the answer I find into the answer the book wants, and why does the book want a different answer to what I find?

For extra help solving, the book, chapter, page and problem number are listed below.

Book: Algebra 2 Common Core (with a robotic lizard on the cover)

Page: 224

Number: 10

Chapter: 4

If someone could help me figure this out, I would be very grateful.

Also, you can most likely expect more questions out of me in the future. I like knowing how to do everything!

Oct 27, 2017

#1
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The book is correct. 16-2x2/2 does equal x2 - 8. What you found equates to the exact same thing. My solution: Both of you are right.

Oct 27, 2017
#2
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What I want to know is how to decide if the answer I found is the answer the book wants. My teacher counts it wrong even if my solution is correct.

Oct 27, 2017
#3
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I guess nobody knows, huh? *sigh* Looks like I'll just have to hope my answers are what the book wants.

Oct 27, 2017
#4
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OBT -  The general rule is to first take out any GCF

So we have

16 - 2x^2

2 [ 8 - x^2 ] which factors as

2  [ √8  -  x ]  [ √8 + x ]        note  √8   = 2√2

2 [ 2√2 - x ]   [ 2√2 + x ]

Note that WolftamAlpha  tends to support the same result as one of its answers :

https://www.wolframalpha.com/input/?i=16+-+2x%5E2

BTW.........the "correct"  factorization  is sometimes ambiguous.....!!!!!

https://www.wolframalpha.com/input/?i=(4%2B+sqrt+(2)x+)+(4+-+sqrt+(2)x)

Oct 27, 2017
#5
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I understand how to solve it, I don't understand how to find any result the book finds. Wolfram never really finds the answer my book wants cause it goes WAAAY too deep into solving.

OfficialBubbleTanks  Oct 27, 2017
edited by OfficialBubbleTanks  Oct 27, 2017
#6
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We have factored it as two binomials....

However....I believe the book is focusing on the factors  being polynomials with integer coefficients

So

16  - 2x^2   is factored as

2 ( 8 - x^2 )

They also appear to want the polynomial inside the parentheses to be written in order of descending powers....so....this gives

-2 ( x^2  - 8)

Does that help  ???

Oct 27, 2017
#7
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Oh my god that is so helpful. Thank you!!!!

OfficialBubbleTanks  Oct 27, 2017