What is factor x^{24}-1 ?

The solution to factor x^{24}-1 is (x^4+1)(x^2+1)(x+1)(x-1)(x^2+x+1)(x^2-x+1)(x^4-x^2+1)(x^8-x^4+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor x^{24}-1

factor

x^{24} - 1

(x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1) (x^{4} - x^{2} + 1) (x^{8} - x^{4} + 1)

Solution steps

x^{24} - 1

Apply exponent rules

= (x^{8})^{3} - 1^{3}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(x^{8})^{3} - 1^{3} = (x^{8} - 1) (x^{16} + x^{8} + 1)

= (x^{8} - 1) (x^{16} + x^{8} + 1)

Factor

x^{8} - 1 : (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1)

= (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1) (x^{16} + x^{8} + 1)

Factor

x^{16} + x^{8} + 1 : (x^{2} + 1 + x) (x^{2} + 1 - x) (x^{4} + 1 - x^{2}) (x^{8} + 1 - x^{4})

= (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1) (x^{2} + 1 + x) (x^{2} + 1 - x) (x^{4} + 1 - x^{2}) (x^{8} + 1 - x^{4})

= (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1) (x^{4} - x^{2} + 1) (x^{8} - x^{4} + 1)

\frac{7}{100} \cdot \frac{10}{3} \cdot \frac{20}{7}

36 - x^{2} = 0

3 x^{2} y - 48 y

- 5 (5 + x) > - 10

15 = x 3

What is factor x^{24}-1 ?
The solution to factor x^{24}-1 is (x^4+1)(x^2+1)(x+1)(x-1)(x^2+x+1)(x^2-x+1)(x^4-x^2+1)(x^8-x^4+1)