Write a polynomial from standard form to factored form

Learn how to write a polynomial from standard form to factored form with a couple of good examples.

Example #1

Write x4 + x3  in factored form

Factor out the GCF, x3

x4 + x= x3(x + 1)

Example #2

Write 3x3 + 15x2 + 18x in factored form

Factor out the GCF, 3x

3x3 + 15x2 + 18x = 3x(x2 + 5x + 6)

Factor x2 + 5x + 6 using the technique in this lesson about factoring trinomials.

Here is a quick summary of the technique:

2 x 3 = 6 and 6 is the constant term

2 + 3 = 5 and 5 is the coefficient of the linear term

You can then use 2 and 3 in the factored form

Therefore, x2 + 5x + 6 = (x + 2)(x + 3)  

3x3 + 15x2 + 18x = 3x(x + 2)(x + 3) 

Example #3

Write 2x3 + 6x2 + -20x in factored form

Factor out the GCF, 2x

2x3 + 6x2 + -20x = 2x(x2 + 3x + -10)

Factor x2 + 3x + -10 using again the technique in the lesson about factoring trinomials.

5 x -2 = -10 and -10 is the constant term

5 + -2 = 3 and 3 is the coefficient of the linear term

You can then use -2 and 5 in the factored form

Therefore, x2 + 3x + -10 = (x - 2)(x + 5)  

3x3 + 15x2 + 18x = 2x(x - 2)(x + 5) 

Recent Articles

  1. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

  2. Binary Number System

    Nov 17, 22 10:53 AM

    This lesson will give you a deep and solid introduction to the binary number system.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes