Réponse :
Bonsoir
Explications étape par étape
A= x8+x+1
A= x8+x7-x7+x6-x6+x5-x5+x4-x4+x3-x3+x2-x2+x+1
A= x8+x7+x6-x7-x6-x5+x5+x4+x3-x4-x3-x2+x2+x+1
A= x6(x2+x+1)-x5(x2+x+1)+x3(x2+x+1)-x2(x2+x+1)+1(x2+x+1)
A= (x2+x+1)(x6-x5+x3-x2+1)
B= x¹⁰ - x⁹ + x⁸ - 2x⁷ + 2x⁶ - 2x⁵ + 2x⁴ - 2x³ + x² - x + 1
B=x¹⁰ - x⁹ + x⁸ - x⁷ - x⁷ + x⁶ + x⁶ - x⁵ - x⁵ + x⁴ + x⁴ - x³ - x³ + x² - x + 1
B=x⁹(x - 1) + x⁷(x - 1) - x⁶(x - 1) + x⁵(x - 1) - x⁴(x - 1) + x³(x - 1) - x²(x - 1) - (x - 1)
B=(x - 1)(x⁹ + x⁷ - x⁶ + x⁵ - x⁴ + x³ - x² - 1)
B=(x - 1)(x⁹ - x⁸ + x⁸ - x⁷ + 2x⁷ - 2x⁶ + x⁶ - x⁵ + 2x⁵ - 2x⁴ + x⁴ - x³ + 2x³ - 2x² + x² - x + x - 1)
B=(x - 1)(x⁸(x - 1) + x⁷(x - 1) + 2x⁶(x - 1) + x⁵(x - 1) + 2x⁴(x - 1) + x³(x - 1) + 2x²(x - 1) + x(x - 1) + (x - 1))
B=(x - 1)²(x⁸ + x⁷ + 2x⁶ + x⁵ + 2x⁴ + x³ + 2x² + x + 1)
B=(x - 1)²(x⁸ + x⁷ + x⁶ + x⁶ + x⁵ + x⁴ + x⁴ + x³ + x² + x² + x + 1)
B=(x - 1)²(x⁶(x² + x + 1) + x⁴(x² + x + 1) + x²(x² + x + 1) + (x² + x + 1))
B=(x - 1)²(x² + x + 1)(x⁶ + x⁴ + x² + 1)
B=(x - 1)²(x² + x + 1)(x⁴(x² + 1) + (x² + 1)))
B=(x - 1)²(x² + x + 1)(x² + 1)(x⁴ + 1)
