- Home
- Grade 12 Math
- Polynomial Functions
Multiplicities of polynomials
- Lesson: 14:20
- Lesson: 24:35
- Lesson: 38:13
Multiplicities of polynomials
Lessons
The multiplicity of a zero corresponds to the number of times a factor is repeated in the function.
⋅ Odd multiplicity: cross the x-axis
⋅ Odd multiplicity (3 or more): changes concavity when passing through x-axis
⋅ Even multiplicity: bounces off the x-axis
⋅ Odd multiplicity: cross the x-axis
⋅ Odd multiplicity (3 or more): changes concavity when passing through x-axis
⋅ Even multiplicity: bounces off the x-axis
- 1.Sketch the graph of the polynomial function.
i) P(x)=x−2
ii) P(x)=(x−2)2
iii) P(x)=(x−2)3
iv) P(x)=(x−2)4
v) P(x)=(x−2)5 - 2.Given that the graph shows a degree-eight polynomial and the zero x=3 has a multiplicity of 2, determine the multiplicity of the zero x=−2.
- 3.Without using a graphing calculator, make a rough sketch of the following polynomial: P(x)=−129077761(x+3)(x+1)2(x−2)3(x−4)4(x−7)5
Do better in math today
3.
Polynomial Functions
3.1
What is a polynomial function?
3.2
Polynomial long division
3.3
Polynomial synthetic division
3.4
Remainder theorem
3.5
Factor theorem
3.6
Rational zero theorem
3.7
Characteristics of polynomial graphs
3.8
Multiplicities of polynomials
3.9
Imaginary zeros of polynomials
3.10
Determining the equation of a polynomial function
3.11
Applications of polynomial functions
3.12
Solving polynomial inequalities
3.13
Fundamental theorem of algebra
3.14
Descartes' rule of signs