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?
Interpret the structure of expressions
Write expressions in equivalent forms to solve problems
|Algebra and Functions||Factoring|
|Passport to Advanced Math||Quadratic and exponential functions (word problems)|
|Polynomials and Rational Expressions||Factoring|
|Product Type||SAT Math|
|SAT Math||Algebra and Functions|
Then we plug in the given functions here, so that's:
x squared minus 16 divided by x to the fourth minus 256.
The numerator and denominator both look like they're begging to be factored.
But let's start with the denominator ….because it has the larger exponent.
Hmmm, what does this ugly number factor into?
Well it kind of looks like a difference of two squares..
x to the fourth is a square of x squared...
And 256 is a perfect square of 16...
So we have x squared minus 16 times x squared plus 16.
Hey! The numerator just so happens to have (x2 - 16) as well.
Instead of factoring that equation even further, we can cancel both the numerator
and one of the factors in the denominator and arrive at 1 over x squared plus 16.