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- Polynomial Functions

Still Confused?

Try reviewing these fundamentals first

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Try reviewing these fundamentals first

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Get Started Now- Intro Lesson13:09
- Lesson: 116:58
- Lesson: 1a1:34
- Lesson: 1b1:08
- Lesson: 1c1:51
- Lesson: 1d1:17
- Lesson: 248:45
- Lesson: 36:44

A polynomial function is a function in the form:

$\bullet$leading coefficient: "${a_n}$", the coefficient of the highest power of x

$\bullet$constant term: "${a_0}$", the term without $x$

$\bullet$degree of the polynomial function: $n$, the highest power of $x$

- IntroductionIntroduction to Polynomial Functions

$\cdot$ What is a polynomial function?

$\cdot$ Exercise:

State the*degree, leading coefficient*and*constant term*for the following polynomial functions:

1) $f(x) = 9x^{5}+7x^{4}-2x^{3}-12x^{2}+x-10$

2) $p(x) = -23x^{18}+37x^{15}-11x^{58}+6$ - 1.
**Recognizing a Polynomial Function**Which of the following are not polynomial functions? Explain.

a)$f(x) = 5x^{2}+4x-3x^{-1}+2$b)$f(x) = -x^{3}+6x^{\frac{1}{2}}$c)$f(x) = (\sqrt x + 3)(\sqrt x - 3)$d)$f(x) = x^{5}+\pi x-\sqrt7 x^{2}+\frac{3}{11}$ - 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

4.

Polynomial Functions

4.1

What is a polynomial function?

4.2

Polynomial long division

4.3

Polynomial synthetic division

4.4

Remainder theorem

4.5

Factor theorem

4.6

Rational zero theorem

4.7

Characteristics of polynomial graphs

4.8

Multiplicities of polynomials

4.9

Imaginary zeros of polynomials

4.10

Determining the equation of a polynomial function

4.11

Applications of polynomial functions

4.12

Solving polynomial inequalities

4.13

Fundamental theorem of algebra

4.14

Descartes' rule of signs