Bonsoir
calculer p(-1) pour p(x) = =-2x³-7x²-2x+3 puis factoriser p(x)
p(-1) = -2(-1)^3 - 7(-1)^2 - 2 * (-1) + 3
P(-1) = -2 * (-1) - 7 + 2 + 3
P(-1) = 2 - 7 + 5
P(-1) = 0
-1 est racine donc p(x) est factorisable par (x + 1)
= (x + 1)(ax^2 + bx + c)
= ax^3 + bx^2 + cx + ax^2 + bx + c
= ax^3 + (a + b)x^2 + (b + c)x + c
a = -2
a + b = -7 => b = -7 - a = -7 + 2 = -5
b + c = -2 => c = -2 - b = -2 + 5 = 3
c = 3
p(x) = (x - 1)(-2x^2 - 5x + 3)
