SAT Math 1.5 Algebra and Functions

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?

AlgebraFactoring
Interpret the structure of expressions
Write expressions in equivalent forms to solve problems
Algebra and FunctionsFactoring
LanguageEnglish Language
Passport to Advanced MathQuadratic and exponential functions (word problems)
PolynomialsFactoring Polynomials
Polynomials and Rational ExpressionsFactoring
Product TypeSAT Math
SAT MathAlgebra and Functions

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).