Polynomial Functions Review

Front

What is a polynomial function?

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Front

What are the operations that can be performed on polynomials?

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The main operations on polynomials include addition, subtraction, multiplication, and division (except by zero). These operations follow specific algebraic rules.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the polynomial equal to zero and solve for the variable. This can involve factoring, using the quadratic formula, or synthetic division.

Front

What is the end behavior of a polynomial function?

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Front

What does it mean for a number to be a zero of a polynomial?

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Front

How do you factor a polynomial completely?

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To factor a polynomial completely, look for common factors, use grouping, or apply special factoring techniques (like difference of squares or sum/difference of cubes) until it cannot be factored further.

Front

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

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A polynomial is a function that consists of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials, which may include negative exponents or division by zero.

Front

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

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Front

What is synthetic division and when is it used?

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Front

How do you determine the multiplicity of a zero?

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The multiplicity of a zero is determined by the exponent of the factor associated with that zero in the polynomial's factored form. A zero with an even multiplicity touches the x-axis, while an odd multiplicity crosses it.