Polynomial expressions

3 Polynomial expressions

An important group of mathematical expressions which use indices are known as polynomials . Examples of polynomials are

$4 x^{3} + 2 x^{2} + 3 x - 7, x^{2} + x, 17 - 2 t + 7 t^{4}, z - z^{3}$

Notice that they are all constructed using non-negative whole number powers of the variable. Recall that $x^{0} = 1$ and so the number $- 7$ appearing in the first expression can be thought of as $- 7 x^{0}$ . Similarly the 17 appearing in the third expression can be read as $17 t^{0}$ .

Key Point 8

Polynomials

A polynomial expression takes the form

a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots + a_{n} x^{n}

where

a_{0}

a_{1}

a_{2}

a_{3}

\dots

a_{n}

are all constants called the coefficients of the polynomial. The number

a_{0}

is also called the constant term . The highest power in a polynomial is called the degree of the polynomial.

Polynomials with low degrees have special names and subscript notation is often not needed:

Polynomial	Degree	Name
$a x^{3} + b x^{2} + c x + d$	$3$	cubic
$a x^{2} + b x + c$	$2$	quadratic
$a x + b$	$1$	linear
$a$	$0$	constant

3 Polynomial expressions

Key Point 8

Task!

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