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Q1. Find k such that f(x) = x⁴ + kx³ + 2 has the factor x + 1.
[removed]   a. -3
[removed]   b. -2
[removed]   c. 3
[removed]   d. 2

Q2. Solve the inequality.

(x - 5)(x² + x + 1) > 0
[removed]   a. (-∞, -1) or (1, ∞)
[removed]   b. (-1, 1)
[removed]   c. (-∞, 5)
[removed]   d. (5, ∞)

Q3. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

f(x) = 8x³ - 10x² + 3x + 5; [-1, 0]
[removed]   a. f(-1) = -16 and f(0) = -5; no
[removed]   b. f(-1) = -16 and f(0) = 5; yes
[removed]   c. f(-1) = 16 and f(0) = -5; yes
[removed]   d. f(-1) = 16 and f(0) = 5; no

Q4. Solve the equation in the real number system.

x⁴ - 3x³ + 5x² - x - 10 = 0
[removed]   a. {-1, -2}
[removed]   b. {1, 2}
[removed]   c. {-1, 2}
[removed]   d. {-2, 1}

Q5. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.

f(x) = x² - 2x - 5
[removed]   a. maximum; 1
[removed]   b. minimum; 1
[removed]   c. maximum; - 6
[removed]   d. minimum; - 6

Q6. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.

f(x) =

[removed]   a. symmetry with respect to the origin
[removed]   b. symmetry with respect to the y-axis
[removed]   c. neither

Q7. Find the domain of the rational function.

f(x) =

.
[removed]   a. {x|x ≠ -3, x ≠ 5}
[removed]   b. {x|x ≠ 3, x ≠ -5}
[removed]   c. all real numbers
[removed]   d. {x|x ≠ 3, x ≠ -3, x ≠ -5}

Q8. Find the domain of the rational function.

g(x) =

[removed]   a. all real numbers
[removed]   b. {x|x ≠ -7, x ≠ 7, x ≠ -5}
[removed]   c. {x|x ≠ -7, x ≠ 7}
[removed]   d. {x|x ≠ 0, x ≠ -49}

Q9. Find all zeros of the function and write the polynomial as a product of linear factors.

f(x) = 3x⁴ + 4x³ + 13x² + 16x + 4
[removed]   a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2)
[removed]   b. f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i)
[removed]   c. f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i)
[removed]   d. f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)

Q10. Use the graph to find the vertical asymptotes, if any, of the function.

[removed]   a. y = 0
[removed]   b. x = 0, y = 0
[removed]   c. x = 0
[removed]   d. none

Q11. Find the power function that the graph of f resembles for large values of |x|.

f(x) = (x + 5)²
[removed]   a. y = x¹⁰
[removed]   b. y = x²⁵
[removed]   c. y = x²
[removed]   d. y = x⁵

Q12. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.

f(x) =

[removed]   a. symmetry with respect to the y-axis
[removed]   b. symmetry with respect to the origin
[removed]   c. neither

Q13. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.

f(x) = -x² - 2x + 2
[removed]   a. minimum; - 1
[removed]   b. maximum; 3
[removed]   c. minimum; 3
[removed]   d. maximum; - 1

Q14. Find the power function that the graph of f resembles for large values of |x|.

f(x) = -x²(x + 4)³(x² - 1)
[removed]   a. y = x⁷
[removed]   b. y = -x⁷
[removed]   c. y = x³
[removed]   d. y = x²

Q15. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

[removed]   a. 25,600 ft²
[removed]   b. 19,200 ft²
[removed]   c. 12,800 ft²
[removed]   d. 6400 ft²

Q16. Find the indicated intercept(s) of the graph of the function.

x-intercepts of f(x) =

[removed] a. (5, 0)
[removed] b.

[removed] c.

[removed]   d. (-5, 0)

Q17. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

f(x) = 9x³ + 8x² - 6
[removed]   a. No; the last term has no variable
[removed]   b. Yes; degree 5
[removed]   c. Yes; degree 3
[removed]   d. Yes; degree 6

Q18. Solve the equation in the real number system.

x³ + 9x² + 26x + 24 = 0
[removed]   a. {-4, -2, -3}
[removed]   b. {2, 4}
[removed]   c. {3, 2, 4}
[removed]   d. {-4, -2}

Q19. Use the graph to find the vertical asymptotes, if any, of the function.

<b
[removed]   a. x = -3, x = 3, x = 0
[removed]   b. x = -3, x = 3, y = 0
[removed]   c. none
[removed]   d. x = -3, x = 3

Q20. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

f(x) = -2x⁴ + 2x² + 4; [-2, -1]
[removed]   a. f(-2) = 20 and f(-1) = 5; no
[removed]   b. f(-2) = -20 and f(-1) = 4; yes
[removed]   c. f(-2) = 20 and f(-1) = -4; yes
[removed]   d. f(-2) = -20 and f(-1) = -4; no