Chapters

A polynomial is an algebraic expression in the form:

P(x) = an xn + an - 1 xn - 1 + an - 2 xn - 2 + ... + a1 x1 + a0

an, an -1 ... a1 , ao... are the numbers and are called coefficients.

n is a natural number.

x is the variable.

ao is the independent term.

### Degree of a Polynomial

The degree of a polynomial P(x) is the greatest degree of the monomials.

### Classification of a Polynomial According to Their Degree

P(x) = 2x² + 3x + 2

## Cubic

P(x) = x³− 2x² + 3x + 2

## Quartic

P(x) = x4 + 2x³− 2x² + 3x + 2

## Quintic

P(x) = 2x5 − x4 + 2x³− 2x² + 3x + 2

## Sextic

P(x) = 3x6 + 2x5 − x4 + 2x³− 2x² + 3x + 2

## Types of Polynomials

### Zero Polynomial

A polynomial that has zero as all its coefficients.

### Homogeneous Polynomial

A polynomial where all its terms or monomials are of the same degree.

P(x) = 2x² + 3xy

### Complete Polynomial

A polynomial which has all the terms ordered from the greatest degree up to the independent degree.

P(x) = 2x³ + 3x² + 5x - 3

### Ordered Polynomial

A polynomial which has its monomials ordered starting from the greatest or smallest degree.

P(x) = 2x³ + 5x - 3

### Equal Polynomials

Two polynomials are equal if:

## 1

The two polynomials have the same degree.

## 2

The coefficients of the terms with the same degree are equal.

P(x) = 2x³ + 5x − 3

Q(x) = 5x − 3 + 2x³

### Similar Polynomials

Two polynomials are similar if they have the same literal part.

P(x) = 2x³ + 5x − 3

Q(x) = 5x³ − 2x − 7

### Evaluating Polynomials

Evaluating a polynomial is to find its numerical value when the variable x is replaced by any number.

P(x) = 2x³ + 5x 3 ; x = 1

P(1) = 2 · 1³ + 5 · 1 − 3 = 2 + 5 - 3 = 4

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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