bsr
Q1
double distributivité + simple distributivité
A(x) = x*5 + x*(-x) - 3*5 - 3*(-x) + 2*x² + 2*(-9)
= 5x - x² - 15 + 3x + 2x² - 18
= x² + 8x - 33
factorisation
puisque x² - 3 = x² - 3² = (x+3) (x-3)
on aura A(x) factorisé par (x-3) :
A(x) = (x-3) [(5-x) + 2(x+3)]
= (x-3) (5 - x + 2x + 6)
= (x-3) (11 +x)
Q2
B(x) = x*1 + x*(-x) + 11*1 + 11*(-x)
= x - x² + 11 - 11x
= -x² - 10x + 11
Q3
comme a²-b² = (a+b) (a-b)
C(x) = (x+2+5) (x+2-5)
= (x+7) (x-3)
Q4
A(x) + C(x) = (x-3) (11 +x) + (x+7) (x-3)
= (x-3) [(11+x) + (x+7)] = (x-3) (2x + 18) = 2 (x-3) (x+9)
et
A(x) - B(x) = (x-3) (11 +x) - (x+11) (1-x)
= (x+11) (x-3 - (1-x))
= (x+11) (2x - 4)
= 2 (x+11) (x-2)
Q5
(x-a) (-x² - 10x+11) = (b-x) (x² + 8x - 33)
je sèche
