Math 3 Fall Final Review

Front

What are the zeros of the function f(x) = (x+2)(x-3)²(x-4)?

Back

The zeros are -2, 3 (multiplicity 2), and 4.

Front

Simplify the expression \( \frac{2x+2}{x+2} \div \frac{4x^2+8x+4}{12x+12} \)

Back

The simplified expression is \( \frac{6}{x+2} \).

Front

What is the factored form of the function represented by the graph?

Back

The equation in factored form is f(x) = (x+4)(x+1)²(x-2)(x-4).

Front

Solve the equation for x: \( \frac{2}{x+2} + \frac{5}{x-2} = \frac{6}{x^2-4} \)

Back

The solution is x = 0.

Front

List the potential real zeros of the polynomial f(x) = 5x³ - x² + 3.

Back

The potential real zeros are ±1/5, ±3/5, ±1, ±3.

Front

What is the definition of a zero of a function?

Back

A zero of a function is a value of x that makes the function equal to zero.

Front

What does multiplicity mean in the context of polynomial zeros?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x.

Front

What is the process for simplifying a complex fraction?

Back

To simplify a complex fraction, multiply the numerator and denominator by the least common denominator (LCD) of the fractions involved.

Front

What is the significance of the factored form of a polynomial?

Back

The factored form reveals the zeros of the polynomial and helps in graphing the function.