Bonjour
A(x) = (2x + 1)² – (2x + 1)(x + 3)
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1) Développer l'expression A(x).
A(x) = (2x + 1)² – (2x + 1)(x + 3)
A (x) = 4x² + 4x + 1 - (2x² + 6x + x + 3)
A (x) = 4x² + 4x + 1 - 2x² - 6x - x - 3
A (x) = 4x² - 2x² + 4x - 6x - x + 1 - 3
A (x) = 2x² - 3x - 2
2) Factoriser l'expression A(x).
A (x) = (2x + 1)² – (2x + 1)(x + 3)
A (x) = (2x + 1) (2x + 1 - x - 3)
A (x) = (2x + 1) (x - 2)
3) En utilisant la forme la plus adaptée, calculer A(x):
a) Pour x = 2.
A (x) = 2x² - 3x - 2
A (2) = 2 * 2² - 3 * 2 - 2
A (2) = 2 * 4 - 6 - 2
A (2) = 8 - 8
A (2) = 0
b) Pour x = 0.
A (x) = 2x² - 3x - 2
A (0) = 2 * 0² - 3 * 0 - 2
A (0) = - 2
c) Pour x =1/3
A (x) = 2x² - 3x - 2
A (1/3) = 2 * (1/3)² - 3 * 1/3 - 2
A (1/3) = 2 * 1/9 - 6/3 - 2
A (1/3) = 2/9 - 12/9 - 18/9
A (1/3) = - 28/9.
