How do I factor a cubed polynomial?

May 2021 4 62 Report

How do I factor a cubed polynomial?

Ok so what are the factors for the cubed polynomial x^3-125?

I'm really confused on how to do it and would appreciate any help!

Thanks.

You use the difference of cubes rule.

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Since, (x^3)^(1/3) = x and 125^(1/3) = 5, we have a = x and b = 5.

x^3 - 125 = (x - 5)[ (x)^2 + (x)(5) + (5)^2 ]

..............= (x - 5)(x^2 + 5x + 25)

Therefore, x^3 - 125 factors to (x - 5)(x^2 + 5x + 25).

Hope this helps!

it's simple ...u have to recognize a^3- b^3= (a-b)(a^2b+ab+ab^2)

all u have to do is to recognize the formula

also 5^3=125