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Teachers & SchoolsSAT 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 | Factoring Interpret the structure of expressions Write expressions in equivalent forms to solve problems |

Algebra and Functions | Factoring |

Language | English Language |

Passport to Advanced Math | Quadratic and exponential functions (word problems) |

Polynomials | Factoring Polynomials |

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 â€¦.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.

Answer's (A).