Writing Polynomials in Standard Form

Writing 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!

Example 1:

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

Solution:

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

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: \(5x^2−9x^5+8x^3−11=
−9x^5+8x^3+5x^2−11 \)

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. \(\color{blue}{5x^2 + 13x – 2x^3}\)

Download Writing Polynomials in Standard Form Worksheet

  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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