How to Write Polynomials in Standard Form? (+FREE Worksheet!)

How to write polynomials in standard form, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

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

How to Write Polynomials in Standard Form? (+FREE Worksheet!)

Tutor-style math help

Write Polynomials in Standard Form: what to notice and how to work it

Polynomials skill

Polynomial problems reward structure. Before expanding, look for degree, leading term, common factors, and familiar products.

What to notice first

Put the polynomial in standard form when possible. The leading term tells end behavior, and factors reveal zeros.

Common student mistake

Do not cancel or combine unlike terms. (x^2), (x), and constants are different kinds of terms.

Key formulas and cues

(a^2-b^2=(a-b)(a+b))

((a+b)^2=a^2+2ab+b^2)

(P(c)=0Rightarrow (x-c)text{ is a factor})

A reliable path

Organize by degreeWrite terms from highest power to lowest power.
Look for structureTry GCF, special products, grouping, or division depending on the expression.
Check with featuresZeros, multiplicity, and end behavior should agree with your algebra.

Worked examples

Combine like terms

Example: (3x^2+5x-x^2+2x)

Group x squared terms.
Group x terms.
Combine each group.

Answer: (2x^2+7x)

Factor a difference of squares

Example: (x^2-25)

Recognize a squared term minus a squared term.
Use a^2 – b^2.
Write conjugate factors.

Answer: ((x-5)(x+5))

Open pop-up practice

Try one before moving on

Try: Factor (x^2+7x+12).

Answer: ((x+3)(x+4)).

Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.

Watch this practice video for additional examples and reinforcement:

Related Topics

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!

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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)

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

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Effortless Math Team

5 days ago

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