# How do you factor x^3 – 1?

##x^3-1=(x-1)(x^2+x+1)=(x-1)(x-w)(x*w^2)## where ##w=-1/2+isqrt(3)/2##

Don't use plagiarized sources. Get Your Custom Essay on
How do you factor x^3 – 1?
Just from \$13/Page

Depending on whether you are factorising you polynomial in ##RR## or ##CC##.

Basically, you should use the factor theorem, so try reals that solves the equation, you should try all integer factors of -1, so +1 and -1.

By trying ##-1##, you see that ##(-1)^2-1=0##, so ##(x-1)## is a factor. Then you need to divide ##x^3-1## by ##x-1## using long division for example.
##(x^3-1)/(x-1)=(x^2+x+1)##.

And finally, you get that ##x^3-1=(x-1)(x^2+x+1)##.

Now you need to factorise a quadratic polynomial, so just use the formula, ##x={ -b+-sqrt(b^2-4ac)}/2##. And you get that ##w## and ##w^2## are the roots. So ##x^3-1=(x-1)(x-w)(x-w^2)##, and now you know that you’re done because by D’Alembert’s Theorem you know that polynomials in ##CC## have as many roots (not necessarily distinct) as the degree of the polynomial, in our case, 3.

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.