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)
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!
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.
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.
I guess nobody knows, huh? *sigh* Looks like I'll just have to hope my answers are what the book wants.
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 :
BTW.........the "correct" factorization is sometimes ambiguous.....!!!!!
Your answer is just as "correct" as the book's......
We have factored it as two binomials....
However....I believe the book is focusing on the factors being polynomials with integer coefficients
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 ???