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Polynomials and Rational Expressions Videos 17 videos
Rational expressions are too complex... it's about time someone simplified them.
It's impressive that these expressions are able to stay so rational even when they're having operations performed on them.
Multiplying rational expressions is as easy as adding the exponents and simplifying. Ta da!
SAT Math 1.5 Algebra and Functions 218 Views
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Description:
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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