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SAT Math 1.5 Algebra and Functions. If f (x) = x2 - 16 and g(x) = x4 - 256, what is f of x divided by g of x?
SAT Math 1.5 Algebra and Functions 218 Views
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SAT Math 1.5 Algebra and Functions. If f (x) = x 2 - 16 and g(x) = x 4 - 256, what is f of x divided by g of x?
- Algebra and Functions / Factoring
- Product Type / SAT Math
- Algebra / Write expressions in equivalent forms to solve problems
- Algebra / Interpret the structure of expressions
- Algebra / Write expressions in equivalent forms to solve problems
- Algebra / Interpret the structure of expressions
- Algebra / Write expressions in equivalent forms to solve problems
- Algebra / Interpret the structure of expressions
- Algebra / Interpret the structure of expressions
- Algebra / Write expressions in equivalent forms to solve problems
- Algebra / Write expressions in equivalent forms to solve problems
- Passport to Advanced Math / Quadratic and exponential functions (word problems)
Transcript
- 00:02
Getting Shmoopy with it...
- 00:04
The question:
- 00:05
If f (x) = x2 - 16 and g(x) = x4 - 256, what is f of x divided by g of x?
- 00:16
And here are the potential answers...
- 00:21
Let's first put in the functions f of x divided by g of x.
Full Transcript
- 00:26
Then we plug in the given functions here, so that's:
- 00:30
x squared minus 16 divided by x to the fourth minus 256.
- 00:35
The numerator and denominator both look like they're begging to be factored.
- 00:42
But let's start with the denominator ….because it has the larger exponent.
- 00:45
Hmmm, what does this ugly number factor into?
- 00:49
Well it kind of looks like a difference of two squares..
- 00:51
x to the fourth is a square of x squared...
- 00:55
And 256 is a perfect square of 16...
- 00:58
So we have x squared minus 16 times x squared plus 16.
- 01:02
Hey! The numerator just so happens to have (x2 - 16) as well.
- 01:07
Instead of factoring that equation even further, we can cancel both the numerator
- 01:12
and one of the factors in the denominator and arrive at 1 over x squared plus 16.
- 01:17
Answer's (A).
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