How to Write Polynomials in Standard Form

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

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.

1. $$\color{blue}{3x^2 – 5x^3}$$
2. $$\color{blue}{3 + 4x^3 – 3}$$
3. $$\color{blue}{2x^2 + x – 6x^3}$$
4. $$\color{blue}{9x – 7x}$$
5. $$\color{blue}{12 – 7x + 9x^4}$$
6. $$\color{blue}{5x^2 + 13x – 2x^3}$$

1. $$\color{blue}{– 5x^3 + 3x^2}$$
2. $$\color{blue}{4x^3}$$
3. $$\color{blue}{–6x^3 + 2x^2 + x}$$
4. $$\color{blue}{2x}$$
5. $$\color{blue}{9x^4 – 7x + 12}$$
6. $$\color{blue}{–2x^3 + 5x^2 + 13x}$$

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