Polynomial Functions

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What is a polynomial function?

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A polynomial function is a mathematical expression that involves a sum of powers in one or more variables multiplied by coefficients. The general form is f(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 does the degree of a polynomial indicate?

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

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the end behavior of the polynomial function.

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What are the transformations of the function f(x) = (x - 3)^2 + 5?

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The function is transformed right 3 units and up 5 units from the parent function f(x) = x^2.

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How do you find the perimeter of a polygon using polynomials?

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To find the perimeter of a polygon, sum the lengths of all sides, which can be expressed as a polynomial if the lengths are given in terms of a variable.

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What is the expression for the total cost of a ticket, seat upgrade, and premium movies if given as (20x + 4), (4x), and (2x + 1)?

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The total cost is represented by the expression (20x + 4) + (4x) + (2x + 1) = 26x + 5.

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How do you calculate the area of a sidewalk given the areas of two rectangles?

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To find the area of the sidewalk, subtract the area of the smaller rectangle from the area of the larger rectangle. If the areas are given as polynomials, perform polynomial subtraction.

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What is the difference between two polynomial profit models?

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To find the difference between two profit models, subtract one polynomial from the other. For example, if Darnell's profit is 2c^2 - 7c - 200 and Stephanie's is c^2 + 8c - 100, the difference is (2c^2 - 7c - 200) - (c^2 + 8c - 100) = c^2 - 15c - 100.

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What is a quadratic polynomial?

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A quadratic polynomial is a polynomial of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms, starting with the term of the highest degree.