Salut !!
2) Développons réduisons et ordonnons :
a. 5t²-2t+t²-7-3.(2t-8)= 5t²+t²-2t-7-6t+24= 6t²-8t+17
b. 9y³-3y+(-2).(4y²+8-7y)-5y³-3y².(7y-2)
=> 9y³-3y-4y²-16+14y-5y³-21y³+6y²
=> -16y³+2y²+11y-16
c. 5.(2z-3)+(7z²-9z³)-(3z⁴+5)-8z-3z²+7z³-z⁴
=> 10z-15+7z²-9z³-3z⁴-5-8z-3z²+7z³-z⁴
=> -4z⁴-2z³+4z²+2z-20
3) a. Calculons la valeur numérique :
T(x)= 3x²+6x⁵+4x³-5 pour x= -1
T(-1)= 3(-1)²+6(-1)⁵+4(-1)³-5
T(x)= 3-6-4-5
T(-1)= -15
Q(x)= 3x + 7x² -5x³ pour x= -2
Q(-2)= 3(-2) + 7(-2)² - 5(-2)³
Q(-2)= -6 +28+40
Q(x)= 62
b. Calculons Q(x) - T(x) et -2T(x) + 3Q(x)
T(x)= 3x² + 6x⁵ + 4x³ - 5
Q(x)= 3x + 7x² - 5x³
Q(x) - T(x) = 3x²+6x⁵+4x³-5 - (3x+7x²-5x³)
Q(x) - T(x) = 3x²+6x⁵+4x³-5 -3x-7x²+5x³
Q(x) - T(x) = (3x²-7x²)+(4x³+5x³)+6x⁵-3x-5
Q(x) - T(x) = -4x² + 9x³ + 6x⁵ - 3x -5
Q(x) - T(x) = 6x⁵ + 9x³ - 4x² - 3x -5
-2T(x) = -2(3x² + 6x⁵ + 4x³ -5)
3Q(x) = 3(3x + 7x² - 5x³)
-2T(x)= -6x² -12x⁵ - 8x³ + 10
-2T(x)= -6x² -12x⁵ - 8x³ + 103Q(x)= 9x + 21x² -15x³
-2T(x)+3Q(x)= -6x²-12x⁵-8x³+10+9x+21x²-15x³
-2T(x)+3Q(x)= (-15x³-8x³)+(21x²-6x²)-12x⁵+10x+9
-2T(x)+3Q(x)= -12x⁵-23x³+15x²+9x+10
