*AA C&C Unit 4 (Modeling Polynomial Functions) TEST

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is p(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

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What are the zeros of a polynomial?

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The zeros of a polynomial are the values of x for which the polynomial function p(x) equals zero. They are also known as the roots of the polynomial.

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How do you find the zeros of a polynomial given its factors?

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To find the zeros of a polynomial given its factors, set each factor equal to zero and solve for x. For example, if the factors are (x + 5)(x - 6)(x - 7), set x + 5 = 0, x - 6 = 0, and x - 7 = 0.

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What is the relationship between the factors and the zeros of a polynomial?

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The zeros of a polynomial correspond to the values of x that make each factor equal to zero. Each factor (x - r) contributes a zero at x = r.

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What is the standard form of a polynomial?

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The standard form of a polynomial is expressed as p(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where the terms are arranged in descending order of the degree.

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What does it mean to simplify a square root of a negative number?

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Simplifying a square root of a negative number involves using the imaginary unit 'i', where i = √(-1). For example, √(-64) simplifies to 8i.

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What is the significance of relative minimum in a polynomial graph?

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A relative minimum is a point on the graph of a polynomial where the function value is lower than the values of the function at nearby points. It indicates a local low point in the graph.

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How can you determine the relative minimum from a graph?

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To determine the relative minimum from a graph, look for the lowest point in a given interval. The coordinates of this point represent the relative minimum.

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What is the process of factoring a polynomial?

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Factoring a polynomial involves expressing it as a product of its factors. This can be done by finding common factors, using the distributive property, or applying special factoring techniques.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial expression. It determines the polynomial's behavior and the number of zeros it can have.