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Polynomial functions
- Intro Lesson13:09
- Lesson: 116:58
- Lesson: 1a1:34
- Lesson: 1b1:08
- Lesson: 1c1:51
- Lesson: 1d1:17
- Lesson: 248:45
- Lesson: 36:44
Polynomial functions
Lessons
A polynomial function is a function in the form:
∙leading coefficient: "an", the coefficient of the highest power of x ∙constant term: "a0", the term without x
∙degree of the polynomial function: n, the highest power of x
- IntroductionIntroduction to Polynomial Functions
⋅ What is a polynomial function?
⋅ Exercise:
State the degree, leading coefficient and constant term for the following polynomial functions:
1) f(x)=9x5+7x4−2x3−12x2+x−10
2) p(x)=−23x18+37x15−11x58+6 - 1.Recognizing a Polynomial Function
Which of the following are not polynomial functions? Explain.
a)f(x)=5x2+4x−3x−1+2b)f(x)=−x3+6x21c)f(x)=(x+3)(x−3)d)f(x)=x5+πx−7x2+113 - 2.Classifying Polynomial Functions by Degree
Complete the chart:
- 3.Classifying Polynomial Functions by Number of Terms
Write a polynomial satisfying the given conditions:
i) monomial and cubic
ii) binomial and linear
iii) trinomial and quartic
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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