When working with polynomials, you should always write them in standard form.

## Related Topics

- How to Multiply Monomials
- How to Multiply and Dividing Monomials
- How to Multiply Binomials
- How to Factor Trinomials
- How to Add and Subtract Polynomials

## Step by step guide to writing polynomials in standard form

- A polynomial function \(f(x)\) of degree \(n\) is of the form

\(f(x)=a_{n} x^{n}+a_{n-1} x_{n-1}+⋯+ a_{1} x+a_{0}\) - The first term is the one with the biggest power!

### Writing Polynomials in Standard Form – Example 1:

Write this polynomial in standard form. \(8+5x^2-3x^3=\)

**Solution:**

The first term is the one with the biggest power: \(8+5x^2−3x^3=−3x^3+5x^2+8\)

### Writing Polynomials in Standard Form – Example 2:

Write this polynomial in standard form. \(5x^2−9x^5+8x^3−11= \)

**Solution:**

The first term is the one with the biggest power: \(5x^2−9x^5+8x^3−11=

−9x^5+8x^3+5x^2−11 \)

### Writing Polynomials in Standard Form – Example 3:

Write this polynomial in standard form. \(-12+3x^2-6x^4=\)

**Solution:**

The first term is the one with the biggest power: \(-12+3x^2-6x^4=-6x^4+3x^2-12\)

## Exercises

### Write each polynomial in standard form.

- \(\color{blue}{3x^2 – 5x^3}\)
- \(\color{blue}{3 + 4x^3 – 3}\)
- \(\color{blue}{2x^2 + x – 6x^3}\)
- \(\color{blue}{9x – 7x}\)
- \(\color{blue}{12 – 7x + 9x^4}\)
- \(\color{blue}{5x^2 + 13x – 2x^3}\)

### Download Writing Polynomials in Standard Form Worksheet

- \(\color{blue}{– 5x^3 + 3x^2}\)
- \(\color{blue}{4x^3}\)
- \(\color{blue}{–6x^3 + 2x^2 + x}\)
- \(\color{blue}{2x}\)
- \(\color{blue}{9x^4 – 7x + 12}\)
- \(\color{blue}{–2x^3 + 5x^2 + 13x}\)