Question

multiply: \\((x + 3)(x^2 + x - 2)\\)

a) \\(x^2 + x - 6\\)
b) \\(x^3 + 3x^2 - 2x - 6\\)
c) \\(x^3 + 4x^2 + x - 6\\)
d) \\(x^2 - x - 6\\)

question 12 (5 points)
which of the following describes the end behavior of the function \\(f(x) = x^4 + 3x^3 - 2x + 7\\)?

a) as \\(x \to -\infty\\), \\(y \to +\infty\\) and as \\(x \to +\infty\\), \\(y \to -\infty\\)
b) as \\(x \to -\infty\\), \\(y \to +\infty\\) and as \\(x \to +\infty\\), \\(y \to +\infty\\)
c) as \\(x \to -\infty\\), \\(y \to -\infty\\) and as \\(x \to +\infty\\), \\(y \to -\infty\\)
d) as \\(x \to -\infty\\), \\(y \to -\infty\\) and as \\(x \to +\infty\\), \\(y \to +\infty\\)

question 13 (5 points)
whats the output of a system modeled by the function \\(f(x) = x^5 - x^4 + 9\\) at \\(x = 2\\)?

a) 24
b) 16
c) 25
d) 30

Explanation:

Multiply the polynomials

Using the Polynomial Multiplication knowledge point

$$
LATEXBLOCK0
$$

Determine the end behavior

Using the Polynomial End Behavior and Leading Coefficient Test knowledge points

$$
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$$

Evaluate the function at x = 2

Using the Algebraic Expression Evaluation knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question 11

• (A) \(x^2 + x - 6\)
• (B) \(x^3 + 3x^2 - 2x - 6\)
• (C) \(x^3 + 4x^2 + x - 6\) (Correct answer)
• (D) \(x^2 - x - 6\)

Question 12

• (A) As \(x \to -\infty\), \(y \to +\infty\) and as \(x \to +\infty\), \(y \to -\infty\)
• (B) As \(x \to -\infty\), \(y \to +\infty\) and as \(x \to +\infty\), \(y \to +\infty\) (Correct answer)
• (C) As \(x \to -\infty\), \(y \to -\infty\) and as \(x \to +\infty\), \(y \to -\infty\)
• (D) As \(x \to -\infty\), \(y \to -\infty\) and as \(x \to +\infty\), \(y \to +\infty\)

Question 13

• (A) 24
• (B) 16
• (C) 25 (Correct answer)
• (D) 30