Réponse :

1) H = (2 x - 1)² + 3 x(2 x - 1)

      = 4 x² - 4 x + 1 + 6 x² - 3 x

      = 10 x² - 7 x + 1

2)  montrer que H peut s'écrire  H = (2 x - 1)(5 x - 1)

il suffit de factoriser H

  H = (2 x - 1)² + 3 x(2 x - 1)

     = (2 x - 1)(2 x - 1 + 3 x)

     = (2 x - 1)(5 x - 1)

3) calculer H

a) x = 0  ⇒  H = 10*0 - 7*0 + 1 = 1

b) x = 3 ⇒ H = 10*3² - 7*3 + 1 = 90 - 21 + 1 = 70

c) x = - 2 ⇒ H = 10*(-2)² - 7*(-2) + 1 = 40 + 14 + 1 = 55

d) x = 1/3 ⇒ H = (2/3 - 1)(5/3 - 1) = - 1/3)*2/3 = - 2/9  

Explications étape par étape

Réponse :

1) H = (2x-1)²+3x(2x-1)

H= 4x²-4x-1+6x²-3x

H=10x²-7x+1

2) H = 2x-1²*3x+2x-1

H = (2x-1) (5x-1)

3) a) H = (2*0-1)²+3*0(2*0-1)

H = (2-1)²+3(2-1)

H = 4-4-1+6-3

H = 2

b) H = (2*3-1)²+3*3(2*3-1)

H = (6-1)²+9(6-1)

H = 36-72+54-9

H = 9

c) H = (2*-2-1)²+3*-2(2*-2-1)

H = (-4-1)²+-6(-4-1)

H = 16+8-1+24+6

H = 5

d) H = (2*1/3-1)²+3*1/3(2*1/3-1)

H = (2/3-1)²+1(2/3-1)

H = 4/9-4/3+2/3-1

H = -2/9-1

Passe une bonne soirée !