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!

OfficialBubbleTanks
Oct 27, 2017

#1**+1 **

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

helperid1839321
Oct 27, 2017

#2**+2 **

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.

OfficialBubbleTanks
Oct 27, 2017

#3**+2 **

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

OfficialBubbleTanks
Oct 27, 2017

#4**+2 **

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.....!!!!!

Your answer is just as "correct" as the book's......

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

CPhill
Oct 27, 2017

#5**+3 **

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

#6**+3 **

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 ???

CPhill
Oct 27, 2017