Polynomial Functions

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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 f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

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What does the leading term of a polynomial indicate?

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The leading term of a polynomial indicates the end behavior of the function as x approaches positive or negative infinity. It is determined by the coefficient and the degree of the polynomial.

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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 end behavior and the number of zeros.

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What are zeros of a polynomial?

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Zeros of a polynomial are the values of x for which the polynomial equals zero. They are also known as roots or x-intercepts.

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. This can involve factoring, using the quadratic formula, or other algebraic methods.

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What is the significance of the coefficient of the leading term?

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The coefficient of the leading term affects the direction of the polynomial's end behavior. A positive coefficient means the polynomial rises to the right, while a negative coefficient means it falls to the right.

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What is end behavior in polynomial functions?

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End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity. It is influenced by the leading term's degree and coefficient.

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What is the difference between even and odd degree polynomials?

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Even degree polynomials have symmetrical end behavior (both ends rise or fall), while odd degree polynomials have opposite end behavior (one end rises and the other falls).

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What is a constant polynomial?

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A constant polynomial is a polynomial of degree 0, which means it has no variable term. Its graph is a horizontal line.

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What is a linear polynomial?

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A linear polynomial is a polynomial of degree 1, which can be expressed in the form f(x) = ax + b, where a ≠ 0. Its graph is a straight line.