Question

which of these is a factor of (x^3 - 3x^2)?

a) (x - 2)
b) (x + 2)
c) (x + 3)
d) (x - 3)

question 10 (5 points)
use pascals triangle to expand ((x + 3)^4).

a) (x^4 + 12x^3 + 54x^2 + 108x + 81)
b) (x^4 - 12x^3 + 54x^2 - 108x + 81)
c) (x^4 + 20x^3 + 90x^2 + 135x + 81)
d) (x^4 - 20x^3 + 90x^2 - 135x + 81)

question 11 (5 points)
for a given function (f(x) = x^5), a translation in the positive (y)-direction of two units is represented by which of the following?

a) (f(x) + 2 = x^5 + 2)
b) (f(x + 2) = (x + 2)^5)
c) (f(x) - 2 = x^5 - 2)
d) (f(x + 2) = (x - 2)^5)

Explanation:

Factor the polynomial

$$ x^3 - 3x^2 = x^2(x - 3) $$

Expand using Pascal's triangle

$$
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$$

Translate the function vertically

$$ g(x) = f(x) + 2 = x^5 + 2 $$

Answer:

Question 9

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

Question 10

• (A) \(x^4 + 12x^3 + 54x^2 + 108x + 81\) (Correct answer)
• (B) \(x^4 - 12x^3 + 54x^2 - 108x + 81\)
• (C) \(x^4 + 20x^3 + 90x^2 + 135x + 81\)
• (D) \(x^4 - 20x^3 + 90x^2 - 135x + 81\)

Question 11

• (A) \(f(x) + 2 = x^5 + 2\) (Correct answer)
• (B) \(f(x + 2) = (x + 2)^5\)
• (C) \(f(x) - 2 = x^5 - 2\)
• (D) \(f(x + 2) = (x - 2)^5\)