EOC Review Math III

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What is a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) = 0. It represents the x-intercepts of the graph of the function.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for x using factoring, the quadratic formula, or numerical methods.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

How do you determine the number of real zeros of a polynomial?

Back

The number of real zeros can be determined by analyzing the degree of the polynomial and using the Descartes' Rule of Signs or by graphing the function.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c).

Front

What is the significance of complex roots in polynomials?

Back

Complex roots occur in conjugate pairs and indicate that the polynomial does not cross the x-axis at those points. They contribute to the overall degree of the polynomial.

Front

What is the process to simplify a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator, cancel out any common factors, and rewrite the expression.

Front

What is the formula for the time taken to complete a task when working together?

Back

If person A can complete a task in a hours and person B in b hours, the time taken to complete the task together is given by: \( \frac{1}{T} = \frac{1}{a} + \frac{1}{b} \) where T is the total time.

Front

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

Back

A polynomial is a function that consists of terms with non-negative integer exponents, while a rational function is the ratio of two polynomials.