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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

27.

Polynomial Functions

27.1

What is a polynomial function?

27.2

Polynomial long division

27.3

Polynomial synthetic division

27.4

Remainder theorem

27.5

Factor theorem

27.6

Rational zero theorem

27.7

Characteristics of polynomial graphs

27.8

Multiplicities of polynomials

27.9

Imaginary zeros of polynomials

27.10

Descartes' rule of signs