How to Write Polynomials in Standard Form

How to Write Polynomials in Standard Form

 Read,4 minutes

What is a Polynomial?

A polynomial can be broken down into two words: "poly" and "nomial," which both signify many  terms, as suggested by the name of the concept. In mathematics, a polynomial is an algebraic or mathematical expression that has at least two terms that are linked together by a mathematical operation. It should be noted that expressions within the polynomial terms could be a constant, a variable, or even a mixed term that contains a co-efficient. A polynomial should also have the power of the variable (let's say x) be an integer rather than a fractional power such as the squared root or the cube root.
For example, 7x12 − 5x + 13 is not a polynomial as the first term has a fraction power of x.

Different Types of Polynomials

Based on the number of terms, there are 3 different types of polynomials. They are monomials, binomials and trinomials. Let’s discuss more about them:

  • Monomial: They consist of just a single term but there is one condition. The term cannot be zero. Also, monomials can all be mixed terms as well as just pure variable terms. Ex: 5x2, 6x3, 69x, etc.
  • Binomial: Binomials consist of just two terms and they must have a mathematical operation in between. Binomials can have mixed terms, pure variable terms, or even pure constant terms in the expression. Ex: 2x2 + 5x3, 3x2 + 8y, xy2 + 2x, etc.
  • Trinomial: Trinomial consist of three terms and between every two terms there is a mathematical operation. Trinomials too can have mixed terms, pure variable terms, and even pure constant terms in the expression. Ex: 2x2 + 3x + 10, 4x3 + 3x2 + 7, 3x2y + 4xy + 6, etc.

Standard Form of Polynomials

The standard form of a polynomial function f(x) of the degree n is:
F(x) = anxn + an−1xn − 1 + …… + a1x + a0, where the first term is the term with the biggest power of the variable (in this case x).
To write a polynomial in the standard form, we must arrange all powers of x in descending order. For example, in 4x2 − 9x3 + 13x − 7, we write the standard form as:
−9x3 + 4x2 + 13x – 7.

Free printable Worksheets

Exercises for Writing Polynomials in Standard Form

1) −20x2 − x + 24x3=

2) x − 2(9x3 − x) − 13x4=

3) x − 2(16x3 − x) − 20x4=

4) −3x2 − 3 + 6x3=

5) −18x2 − 7 + 19x3=

6) −2(7x3 − x) − 9x4=

7) 16x2−18x3=

8) −2(22x3 − x) − 24x4=

9) −5x2 − x + 9x3=

10) −6x2 − x + 10x3=

 
1) −20x2 − x + 24x3= 24x3−20x2 − x
2) x − 2(9x3 − x) − 13x4= −13x4−18x3 + 3x
3) x − 2(16x3 − x) − 20x4= −20x4−32x3 + 3x
4) −3x2 − 3 + 6x3= 6x3−3x2 − 3
5) −18x2 − 7 + 19x3= 19x3−18x2 − 7
6) −2(7x3 − x) − 9x4= −9x4−14x3 + 2x
7) 16x2−18x3= −18x3+16x2
8) −2(22x3 − x) − 24x4= −24x4−44x3 + 2x
9) −5x2 − x + 9x3= 9x3−5x2 − x
10) −6x2 − x + 10x3= 10x3−6x2 − x

Writing Polynomials in Standard Form Practice Quiz