Polynomials Graphs

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

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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.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.

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How do you find the factors of a polynomial?

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To find the factors of a polynomial, you can use methods such as synthetic division, factoring by grouping, or the Rational Root Theorem.

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What is the Rational Root Theorem?

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What is the significance of the x-intercepts of a polynomial graph?

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The x-intercepts of a polynomial graph represent the zeros of the polynomial, indicating where the graph crosses the x-axis.

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What does it mean for a polynomial to have a repeated root?

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A repeated root occurs when a polynomial has a factor that appears more than once, which affects the graph's behavior at that root, causing it to touch the x-axis but not cross it.

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How can you determine the end behavior of a polynomial function?

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The end behavior of a polynomial function can be determined by the leading term's degree and coefficient: if the degree is even, both ends go in the same direction; if odd, they go in opposite directions.

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What is the difference between a polynomial and a rational function?

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A polynomial is a function that consists only of non-negative integer powers of x, while a rational function is a ratio of two polynomials.

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What is the vertex form of a quadratic polynomial?

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