Question

Exercice 1:

On considère l'expression A(x) = (x + 5)²-16 pour tout réel x.
1. Déterminer la forme développée de A(x).
2. Déterminer la forme factorisée de A(x).
3. Utiliser la forme la plus adaptée pour répondre aux questions suivam
a) Calculer A(-6).
b) Calculer A(√2).
c) Résoudre A(x) = 0.
d) Résoudre A(x) = -16.
e) Résoudre A(x) = 9.

Answer 1

To expand and factorize the expression (x + 5)² - 16, and solve equations involving A(x)

Step-by-step explanation:

To find the expanded form of A(x), we can use the formula (a + b)² = a² + 2ab + b². In this case, a = x and b = 5. So, applying the formula, we have:

A(x) = (x + 5)² - 16

A(x) = x² + 2(5)(x) + 5² - 16

A(x) = x² + 10x + 25 - 16

A(x) = x² + 10x + 9

To find the factored form of A(x), we can use the formula (a + b)(a - b) = a² - b². In this case, a = x + 5 and b = 4. So, applying the formula, we have:

A(x) = (x + 5)(x - 4)

a) To calculate A(-6), we substitute x = -6 into the function: A(-6) = (-6)² + 10(-6) + 9

b) To calculate A(√2), we substitute x = √2 into the function: A(√2) = (√2)² + 10(√2) + 9

c) To solve A(x) = 0, we set x² + 10x + 9 = 0 and solve for x.

d) To solve A(x) = -16, we set x² + 10x + 9 = -16 and solve for x.

e) To solve A(x) = 9, we set x² + 10x + 9 = 9 and solve for x.

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