Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Functions
A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The degree of a polynomial is determined by the highest power of the variable. For example, a polynomial of degree 3 can be expressed in the form ƒ(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are real coefficients.
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Zeros of a Polynomial
The zeros (or roots) of a polynomial are the values of x for which the polynomial evaluates to zero. For a polynomial of degree 3, there can be up to three real zeros. In this case, the given zeros are -2, 1, and 0, which means the polynomial can be expressed as ƒ(x) = k(x + 2)(x - 1)(x), where k is a non-zero constant.
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Evaluating Polynomial Functions
Evaluating a polynomial function involves substituting a specific value for the variable and calculating the result. In this problem, we need to ensure that the polynomial satisfies the condition ƒ(-1) = -1. This means substituting -1 into the polynomial and solving for the constant k to meet this requirement, ensuring the function meets all specified conditions.
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