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- UK Year 12 Maths
- Polynomial Functions

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Intro Lesson13:09
- Lesson: 1a1:34
- Lesson: 1b1:08
- Lesson: 1c1:51
- Lesson: 1d1:17
- Lesson: 26:44

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 Number of Terms**

Write a polynomial satisfying the given conditions:

i) monomial and cubic

ii) binomial and linear

iii) trinomial and quartic

11.

Polynomial Functions

11.1

What is a polynomial function?

11.2

Polynomial long division

11.3

Polynomial synthetic division

11.4

Remainder theorem

11.5

Factor theorem

11.6

Rational zero theorem

11.7

Characteristics of polynomial graphs

11.8

Multiplicities of polynomials

11.9

Imaginary zeros of polynomials

11.10

Determining the equation of a polynomial function

11.11

Applications of polynomial functions

11.12

Solving polynomial inequalities

11.13

Solving polynomial equations by iteration

11.14

Fundamental theorem of algebra

11.15

Descartes' rule of signs