Rational Functions with A Hole in the Graph Example 1

Rational Functions Example 3.

Rational Functions Removable Discontinuity of a Hole on Graph Example 4.

Rational Functions.

Vertical Asymptotes.

Horizontal Asymptotes.

Slant Asymptote.

Removable Discontinuity.

Holes in the Graph.

Long Division and Synthetic Division.

Graphing Rational Functions with a Slant Asymptote.

The Remainder and the Factor Theorems. Synthetic Division. Long Division. With Five Examples.

0:00 Introduction.

2:51 P(x)=x^2-8x+22 and (x-a) =x-5

4:14 P(x)=q(x) (x-a)+r

6:29 Example 1: Use Synthetic Substitution to find f(-3), if f(x) - -2 x^4 +3 x^2-15 x+ 9.

9:30 Example 2: Show that (x+8) is a factor of 2x^3+15x^2-11x-24.

12:47 Example 3: Given the Polynomial x^3-x^2-10x-8, and one of the factors " (x+2)", find the remaining factors of the Polynomial.

14:43 Example 4: Given the Polynomial x^3+2x^2-x-2, and one of the factors " (x+2)", find the remaining factors of the Polynomial.

16:20 Example 5: Given the Polynomial x^3-19x+30, and one of the factors " (x-2)", find the remaining factors of the Polynomial.