5. The simplified form of [tex]$2 \sqrt{2}$[/tex] is [tex]$2 \sqrt{2}$[/tex].

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

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

8. If [tex]f(x) = x^3 + 3x[/tex] and [tex]g(x) = x - x^2[/tex], then [tex]f(x) - g(x)[/tex] simplifies to a new polynomial.

9. Let [tex]f(x) = 55x^{200} + 50[/tex] and [tex]d(x) = x+1[/tex]. The remainder when [tex]f(x)[/tex] is divided by [tex]d(x)[/tex] is obtained using the Remainder Theorem.

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

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

13. The value of [tex](3)^{-3}[/tex] is [tex]\frac{1}{27}[/tex].

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Choose the correct answer:

**Which of the following is a polynomial function?**

A. [tex]f(x) = |x|[/tex]
B. [tex]k(x) = 7[/tex]
C. [tex]l(x) = \sqrt{5}x + \sqrt{2}[/tex]
D. [tex]h(x) = (x-1)(x+1)[/tex]

**The degree of the polynomial function [tex]f(x) = (x+3)(x^3+1)[/tex] is:**

A. 4
B. 3
C. 1
D. 2

**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^5[/tex]

**What is the coefficient of [tex]x^3[/tex] in the expression [tex]\frac{7 - 12x^3 + 4x^4 - 2x^4 + 8}{4}[/tex]?**

A. 4
B. -3
C. -12
D. 2

**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(x) - g(x)[/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]

**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