POLYNOMIAL FUNCTIONS REVIEW

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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 ≠ 0.

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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. For example, in P(x) = 3x^4 - 7x^2 + 2, the degree is 4.

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How do you find the zeros of a polynomial function?

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To find the zeros of a polynomial function, set the polynomial equal to zero and solve for the variable. The solutions are the x-values where the graph intersects the x-axis.

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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. For example, in P(x) = 4x^3 + 2x^2 - 5, the leading coefficient is 4.

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What is the end behavior of a polynomial function?

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The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term.

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What are x-intercepts?

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X-intercepts are the points where the graph of a function crosses the x-axis. They occur where the function equals zero.

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How do you determine the number of x-intercepts from a polynomial?

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The number of x-intercepts can be determined by the degree of the polynomial and the nature of its roots. A polynomial of degree n can have up to n x-intercepts.

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What is the significance of the leading term in a polynomial?

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The leading term determines the end behavior of the polynomial function and influences the shape of the graph.

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What is a factored form of a polynomial?

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A polynomial is in factored form when it is expressed as a product of its linear factors. For example, P(x) = (x - 1)(x + 2)(x - 3) is a factored form.

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What does it mean for a polynomial to be in standard form?

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A polynomial is in standard form when its terms are arranged in descending order of degree. For example, P(x) = 2x^3 + 3x^2 - x + 5 is in standard form.