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)
Jan 12, 22 07:48 AM
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