Question

Descompuneti in factori expresia x^5+x+1

va roog e pentru pregatire​

Answer 1

Salut,

x^5+x+1=(x^5-x^4+x^2)+(x^4-x^3+x)+(x^3-x^2+1)=x^2(x^3-x^2+1)+x(x^3-x^2+1)+(x^3-x^2+1)=(x^3-x^2+1)(x^2+x+1)

$by \\ 7646$

Answer 2

x⁵ + x + 1  =

= x⁵ - x⁴ + x⁴ - x³ + x³ - x² + x² + x + 1

= x⁴(x - 1) + x³(x - 1) + x²(x - 1) + x² + x + 1

= (x - 1)·(x⁴ + x³ + x²) + (x² + x + 1)

= (x - 1)·(x²)(x² + x + 1) + (x² + x + 1)

= (x² + x + 1)·[1 + (x - 1)x²)]

= (x² + x + 1)·(1 + x³ - x²)

= (x² + x + 1)·(x³ - x² + 1)

= (x³ - x² + 1)·(x² + x + 1)