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) 

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    Learn how to write a polynomial from standard form to factored form

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