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

**Example #1**

Write x^{4} + x^{3} in factored form

Factor out the GCF, x^{3}

x^{4} + x^{3 }= x^{3}(x + 1)

**Example #2**

Write 3x^{3} + 15x^{2} + 18x in factored form

Factor out the GCF, 3x

3x^{3} + 15x^{2} + 18x = 3x(x^{2} + 5x + 6)

Factor x^{2} + 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, x^{2} + 5x + 6 = (x + 2)(x + 3)

3x^{3} + 15x^{2} + 18x = 3x(x + 2)(x + 3)

**Example #3**

Write 2x^{3} + 6x^{2} + -20x in factored form

Factor out the GCF, 2x

2x^{3} + 6x^{2} + -20x = 2x(x^{2} + 3x + -10)

Factor x^{2} + 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, x^{2} + 3x + -10 = (x - 2)(x + 5)

3x^{3} + 15x^{2} + 18x = 2x(x - 2)(x + 5)