Polynomials

Maths: Edexcel A Level Pure Maths, topic 2.4.1

Polynomials

You need to be able to name polynomials and give their degrees.

$Terminology$

Terminology

When a term in an expression is of the form $ax^m$ , where $a$ is a constant and $m$ is a whole number, it is called a monomial.
For example, $3x^5$ is a monomial.
Similarly, a binomial is the sum or difference of two monomials.
$2x + 6x^4$ is a binomial.
A trinomial is the sum or difference of three monomials.
$1 + 4x - 5x^2$ is a trinomial.

$Polynomials$

Polynomials

The general term for the sums of monomials is polynomials.
$1-2x + 4x^2 -17x^5 + 3x^{12}$ is a polynomial.
Polynomials can always be written in the form:
$a_n x^n + a_{n-1}x^{n-1}+ ... + a_2x^2 + a_1x + a_0$
Where $a_i$ are real numbers that we call coefficients.

Degree

Degree

The degree of a term is the exponent of its variable.
The degree of a constant is 0, as any constant $a = ax^0$ .
The degree of a polynomial is the highest degree of all its terms.
The degree of $3x^3-5x+7$ is $3$ .

Test yourself on Polynomials

Which phrase best describes the expression $-5a^4$ ?
Which phrase best describes the expression $8x^2-7x-9$ ?
Which phrase best describes the expression $n$ ?

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