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The problem asks to identify the quadratic polynomial functions (polynômes de degré 2) from the given options and to specify their coefficients.

Let's analyze each function:

a) \( f(x) = (x - 1)^2 \)

Expand \( f(x) \):

\[
f(x) = (x - 1)(x - 1) = x^2 - 2x + 1
\]

This is a quadratic polynomial. The coefficients are:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = -2 \) (coefficient of \( x \))
- \( c = 1 \) (constant term)

b) \( g(x) = (x + 1)(x - 1) \)

Expand \( g(x) \):

\[
g(x) = x^2 - 1
\]

This is a quadratic polynomial. The coefficients are:
- \( a = 1 \)
- \( b = 0 \)
- \( c = -1 \)

c) \( h(x) = (x + 1)^2 - (x - 1)^2 \)

Let's expand and simplify \( h(x) \):

First, expand \( (x + 1)^2 \) and \( (x - 1)^2 \):

\[
(x + 1)^2 = x^2 + 2x + 1
\]
\[
(x - 1)^2 = x^2 - 2x +

Parmi les fonctions ci-dessous, indiquer les fonctions polynômes de degré 2, en précisant ses coefficients. a) f(x) = (x - 1)^2 b) g(x) = (x + 1)(x - 1) c) h(x) = (x + 1)^2 - (x - 1)^2

Learn how to identify quadratic polynomials from a set of given functions and determine their coefficients. This problem involves polynomial expansion, factoring, and understanding the properties of quadratic equations. Suitable for students in Grades 8-10.

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