Ch 5: Polynomial and Rational Functions.
Ch 5: Polynomial and Rational Functions.
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.