How to Classify Polynomials

Read,3 minutes

Polynomials appear in lots of forms. They may differ via the number of terms, or monomials, which make up the polynomial, plus they additionally might differ via the degrees of the monomials in the polynomial. At this time, we are going to look at several methods of classifying polynomials. Firstly, we’ll categorize polynomials via the number of terms in the polynomial. After that, we’ll categorize them via the monomial that has the biggest exponent.

Find Polynomials, Monomials, Binomials, and Trinomials

Monomials, or sums and/or difference of monomials, is known as polynomials. Polynomials comprising $2$ terms, like $4x \ + \ 6$ , are known as binomials. If the polynomial contains $3$ terms, like in $7x^2 \ + \ 2x \ + \ 3$ , it is known as a trinomial.
polynomial—Monomial, or 2 or more monomials, combined by addition or subtraction (“poly” stands for many)
monomial—Polynomial with precisely one term (“mono” stands for one)
binomial—Polynomial with precisely $2$ terms (“bi” stands for two)
trinomial—Polynomial with precisely $3$ terms (“tri” stands for three)

Here are a few examples of polynomials:

Polynomial	$z \ + \ 4$	$2b^2 \ - \ 3b \ + \ 9$	$7q^6 \ - \ 2q^5 \ - \ 3q^3 \ + \ 9$
Monomial	$r^7$	$35$	$-11x^4$
Binomial	$q^2 \ - \ 5$	$-3p \ + \ p^4$	$6y \ + \ 3$
Trinomial	$6y \ + \ 3y^7 \ - \ 2y^9$	$8q^5 \ + \ 3q^2 \ - \ 5q$	$z^3 \ - \ 5z \ + \ 4z^4$

Note that every monomial, binomial, and trinomial is additionally a polynomial. They’re special members in the family of polynomials which have special names. The words ‘monomial’, ‘binomial’, and ‘trinomial’ are used whenever you want to refer to these special polynomials, then you may call all the rest of them ‘polynomials’.

Figuring out the Degree of Polynomials

It is possible to calculate a polynomial’s degree via determining the highest power of the variable which occurs in it. You can classify polynomials using the polynomial’s degree. The polynomial’s degree is the degree of its highest degree term. Therefore, the degree of $-2y \ + \ y^4 \ - \ y^6$ is $6$ .

Polynomials are said to be written in standard form whenever the terms are placed from the highest to the lowest degree. Whenever they are written using the standard form it’s simple to figure out the polynomial’s degree. The term having the highest degree is known as a leading term since it’s written first in the standard form. The leading term’s coefficient is known as a leading coefficient.

Free printable Worksheets

Exercises for Classifying Polynomials

1) $-8x + 7$ $\ \Rightarrow \$

2) $9x^6 + 4x^5 - 6x^4$ $\ \Rightarrow \$

3) $6x + 2$ $\ \Rightarrow \$

4) $-1x + 2$ $\ \Rightarrow \$

5) $-6x^2 + 6x - 7$ $\ \Rightarrow \$

6) $8x^2 + 1x - 4$ $\ \Rightarrow \$

7) $-12x^2 + 5x - 4$ $\ \Rightarrow \$

8) $-8x^4 + 2x^3 - 1x^2 + x$ $\ \Rightarrow \$

9) $5x^2 - 6x^3$ $\ \Rightarrow \$

10) $7x^4 + 7x^3 - 3x^2 + x$ $\ \Rightarrow \$

Answers

- 8 x + 7

$-8x + 7$

\Rightarrow

$\ \Rightarrow \$ Linear binomial

9 x^{6} + 4 x^{5} - 6 x^{4}

$9x^6 + 4x^5 - 6x^4$

\Rightarrow

$\ \Rightarrow \$ Sixth degree trinomial

6 x + 2

$6x + 2$

\Rightarrow

$\ \Rightarrow \$ Linear binomial

- 1 x + 2

$-1x + 2$

\Rightarrow

$\ \Rightarrow \$ Linear binomial

- 6 x^{2} + 6 x - 7

$-6x^2 + 6x - 7$

\Rightarrow

$\ \Rightarrow \$ Quadratic trinomial

8 x^{2} + 1 x - 4

$8x^2 + 1x - 4$

\Rightarrow

$\ \Rightarrow \$ Quadratic trinomial

- 12 x^{2} + 5 x - 4

$-12x^2 + 5x - 4$

\Rightarrow

$\ \Rightarrow \$ Quadratic trinomial

- 8 x^{4} + 2 x^{3} - 1 x^{2} + x

$-8x^4 + 2x^3 - 1x^2 + x$

\Rightarrow

$\ \Rightarrow \$ Quartic polynomial with four terms

5 x^{2} - 6 x^{3}

$5x^2 - 6x^3$

\Rightarrow

$\ \Rightarrow \$ Cubic binomial

10)

7 x^{4} + 7 x^{3} - 3 x^{2} + x

$7x^4 + 7x^3 - 3x^2 + x$

\Rightarrow

$\ \Rightarrow \$ Quartic polynomial with four terms

How to Classify Polynomials