Question 1

Which of the following best describes the end behavior of the graph of a quartic function with a negative leading coefficient?

Accepted Answer

Both ends open down.

Question 2

Given the polynomial $$f(x) = 4x^5$ - 2x^3$ + x - 7$$, what is the degree and leading coefficient of the polynomial?

Accepted Answer

Degree: 5, Leading coefficient: 4

Question 3

Simplify the following rational expression: $$\frac{x^2$ - 9}{x^2$ - 6x + 9}$$

Accepted Answer

$$\frac{(x-3)(x+3)}{(x-3)^2$}$$

Question 4

Which of the following is the correct first step in dividing $$2x^3$$ + $$5x^2 - x + 4$ by x - 2$ using long division?

Accepted Answer

Divide $$2x^3 by$$ $$x to $$get $$2x^2.$$

Question 5

A cubic function has the equation $$f(x) = -x^3$ + 2x^2$ + 5x - 1. $$What is the end behavior of its graph?

Accepted Answer

Left end opens up, right end opens down.

Question 6

What is the least common denominator (LCD) of the rational expressions $$\frac{3}{x^2$ - 4}$$ and $$\frac{5}{x^2$ - 2x}$$?

Accepted Answer

$$(x-2)(x+2)(x)$$

Question 7

Simplify the complex fraction: $$\frac{\frac{5}{2y} + \frac{3}{y}}{\frac{1}{4} + \frac{1}{3y}}$$

Accepted Answer

$$\frac{11y}{2y + 3}$$

Question 8

If a polynomial function of degree 4 has 3 turning points, which of the following statements is true?

Accepted Answer

The function can have at most 4 x-intercepts.

Question 9

Which of the following is the correct way to multiply $$\frac{x^2$ - 1}{x + 2}$$ and $$\frac{x + 2}{x - 1}$$?

Accepted Answer

$$\frac{(x^2$ - 1)}{(x - 1)}$$

Question 10

A real-world scenario: The number of older workers in millions is modeled by $$y = 0.0001x^3$ - 0.01x^2$ + 0.5x + 2$$, where $$x is $$years after 1960. Estimate the number of older workers in 2025.

Accepted Answer

About 13.6 million

Question 11

Which of the following statements about the graph of a polynomial function of degree $$n is $$always true?

Accepted Answer

It has at most $$n-1$$ turning points.

Question 12

Divide $$2x^2 + 3x + 1$ by x + 1$ using long division. What is the quotient?

Accepted Answer

Question 13

Which of the following best describes the end behavior of the graph of $$f(x) = -2x^4$ + 3x^2$ - 5$$?

Accepted Answer

Both ends open down.

Question 14

Which of the following is the correct simplified form of $$\frac{2}{x} \div \frac{4}{x^2$}$$?

Accepted Answer

$$\frac{x}{2}$$

Question 15

If the graph of a polynomial function has 2 turning points and 3 x-intercepts, what is the minimum possible degree of the polynomial?

Accepted Answer

3

Question 16

Which of the following is the correct way to add $$\frac{2}{x}$$ and $$\frac{3}{x+1}$$?

Accepted Answer

$$\frac{2(x+1) + 3x}{x(x+1)}$$

Question 17

Which of the following is true about the number of turning points for a polynomial of degree $$n$$?

Accepted Answer

It has at most $$n-1$$ turning points.

Question 18

Given the complex fraction $$\frac{2 - \frac{1}{x}}{2x - \frac{3x}{x+1}}$$, which of the following is the correct first step to simplify it?

Accepted Answer

Find the LCD for all fractions in the numerator and denominator

Higher-Degree Polynomial and Rational Functions: Study Notes

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