AP Precalculus / Unit 1: Polynomial and Rational Functions
1.11 Equivalent Representations of Polynomial and Rational Expressions
Notes
Rewrite expressions to reveal features:
- Factored form shows zeros.
- Standard form shows end behavior and the $y$-intercept.
- Long division of a rational function shows a slant asymptote.
- Binomial theorem / Pascal's triangle expands $(a+b)^n$.
Practice
$x^2-5x+6$ in factored form:
Multiply to 6, add to $-5$.
The coefficients of $(a+b)^4$ are:
Row 4 of Pascal's triangle.
$\displaystyle \frac{x^2+3x+5}{x+1}$ divides to $\displaystyle x+2+\frac{3}{x+1}$. The slant asymptote is:
The polynomial part.
Ready for more? Take the Unit 1 test.