answersLogoWhite

0


Best Answer

One obvious root of this is x = 1, so (x-1) is a factor.

Use long division of (x3 -1)/(x-1) and the quotient (x2 + x + 1) will be another factor.

So (x3 -1) = (x-1)(x2 + x + 1).

Remember that a cubic polynomial will always have 3 roots. It will either be 1 pure real root and 2 complex roots, or 3 pure real root. In this case (x2 + x + 1) has two complex roots, and cannot be factored with real numbers.

In general, any odd-powered polynomial (3rd order, 5th order etc), will have at least one pure real root, and then pairs of either pure-real or complex roots.

Any even powered polynomial (2nd order, 4th order, etc) will have pairs of either pure-real, or complex roots.

Don't be fooled if you only find one root. Example: (x2 + 2x + 1) actually has a double root, as it is factored into (x+1)(x+1).

User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

RossRoss
Every question is just a happy little opportunity.
Chat with Ross
JudyJudy
Simplicity is my specialty.
Chat with Judy
EzraEzra
Faith is not about having all the answers, but learning to ask the right questions.
Chat with Ezra

Add your answer:

Earn +20 pts
Q: How do you factor out x cubed minus 1?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

How do you factor x minus 1 cubed minus x plus 1 cubed?

(x - 1)(x - 1)(x - 1) - (x + 1)(x + 1)(x + 1)


How do you factor variable cubed minus the variable?

x(x + 1)(x -1)


Factor x cubed minus one?

(x - 1)(x^2 + x + 1)


How do you factor the expression x cubed minus 1?

(x - 1)(x^2 + x + 1)


How do you factor x cubed minus 27?

t3-1/27


How do you factor x cubed minus x squared plus x?

Factor out the GCF and get X(X2-X+1).


How do you factor x cubed minus five x squared plus x minus 5?

(x - 5)(x^2 + 1)


What is x minus 1 cubed?

xcubed-1 Answer::(X-1)(Xsquared+X+1) when you factor xcubed minus a number its the same thing as x cubed minus y cubed and x cubed minus y cubed factors to:: (x-y)(xsquared+xy+y squared) the first factor, (x-y), is the cubed root of the first and the cubed root of the second, so in the answer i have (x-1), which is x cubed minus one cubed :) the second factor, (xsquared+xy+ysquared), you take the first number squared, Xsquared, then the first and second one multiplied together, XY, and then the second number squared, Ysquared, so in the answer i have (xsquared+x+1), which is x squared, then x times 1 which is just x, and positive 1, which is negative 1 squared :) x^3 - 1


How do you factor 9x cubed plus 18x squared minus x minus 2?

(x + 2)(3x - 1)(3x + 1)


How do you factor the expression x cubed minus x squared plus x minus 3?

x³ - x² + x - 3 (x² + 1)(x - 1) - 2


How do you factor X cubed minus 20x squared plus 19x?

x(x - 19)(x - 1)


How do you factor 64 x cubed minus y cubed?

64 x cubed minus y cubed is (4x - y)(16x^2 + 4xy + y^2)