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 + x³ = 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)