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Math question: How to factor x^5 - 1?
The answer is (x-1)(x^5 + x^4 + x^3 + x^2 + x + 1) by the way.
How do you do that?
The chapter I'm in doesn't involve long division. There must be a different way.
2 Answers
- Dragon.JadeLv 710 years agoFavorite Answer
Hello,
P(x) = x^5 - 1
= x^5 - x^4 + x^4 - x³ + x³ - x² + x² - x + x - 1
= (x^4)(x - 1) + x³(x - 1) + x²(x - 1) + x(x - 1) + (x - 1)
= (x - 1)(x^4 + x³ + x² + x + 1)
QED.
Logically,
Dragon.Jade :-)
- spiffin456Lv 710 years ago
You can see that if you put x = 1, x^5 - 1 = 0, so (x - 1) must be a factor.
To find the other factor you have to do long division, it's a bit tedious and too long to set out here.
