5. Simplify the expression given by [tex]1 = 5[/tex].

6. Given [tex]f(x)[/tex], find the vertex of the graph of [tex]f(x) = (n+k)^2 + c[/tex].

7. For the polynomial function [tex]f(x) = 3x^4 + 2x^3 - 3[/tex], what is the leading coefficient?

8. In the polynomial function, let [tex]f(x) = x^3 + 3x[/tex] and [tex]g(x) = x - x^2[/tex]. Evaluate [tex]f(x), g(x)[/tex].

9. Let [tex]f(x) = 55x^{200} + 50[/tex] and [tex]d(x) = x + 1[/tex]. Find the remainder of [tex]f(x)[/tex] when divided by [tex]d(x)[/tex].

11. If [tex]f(e) = 0[/tex], then [tex](x-c)[/tex] is a factor of the polynomial.

12. Let [tex]g(x) = 5(x+\sqrt{2})^2(x+2^3)(1+3x)[/tex]. Determine the multiplicity of [tex]g(x)[/tex].

The value of [tex](3)^{-3}[/tex] is:

III. Choose the correct answer:

14. Which of the following is a linear function?
A. [tex]f(x) = |x|[/tex]
B. [tex]k(x) = 7[/tex]
C. [tex]l(x) = \sqrt{5}x + \sqrt{2}[/tex]

15. The polynomial function [tex]f(x) = (x+3)(x^3+1)[/tex] equals:
D. [tex]h(x) = (x-1)(x+1)[/tex]

The degree of [tex]f(x)[/tex] is:
A. 4
B. 3
C. 1
D. 2

16. Which of the following is a polynomial function?
A. [tex]g(x) = 4x^{-2} + 3x - 7[/tex]
B. [tex]k(x) = 2^x[/tex]
C. [tex]\sqrt{x}[/tex]
D. [tex]3 - x^6[/tex]

17. In the expression [tex]\frac{7 - 12x^3 + 4x^4 - 2x^4 + 8}{4}[/tex], what is the coefficient of [tex]x^3[/tex]?
A. 4
B. -3
C. -12
D. 2

18. If [tex]f(x) = -2x^3 + 5x^2 + 3x + 2[/tex] and [tex]g(x) = -2x^3 + 4x^2 + 8x + 7[/tex], then what is the value of [tex]f - g[/tex]?
A. [tex]x^2 - 5x + 9[/tex]
B. [tex]x^2 + 5x + 9[/tex]
C. [tex]x^2 - 5x - 7[/tex]
D. [tex]x^2 - 5x - 5[/tex]

19. If [tex]x^2 - x + 3[/tex] is divided by [tex]x - c[/tex] and [tex]c = -2[/tex], what is the remainder?
A. 7
B. -7
C. 9
D. 6