Question

question 9 (multiple choice worth 1 points)
(02.01r)

which of the following is a factor of \\(3x^3 + 18x^2 + 27x\\)?

• \\(9x\\)
• \\(x^3\\)
• \\(x + 3\\)
• \\(x - 3\\)

question 10 (multiple choice worth 1 points)
(02.01r)

factor completely \\(2c^5 + 44c^4 + 242c^3\\).

• \\(2c^3(c + 11)^2\\)
• \\(2(c + 11)^2\\)
• \\(2c^3(c + 11)(c - 11)\\)
• \\(2c^3(c^2 + 22c + 121)\\)

Explanation:

Factor out the greatest common factor of Question 9

Using the Greatest Common Factor knowledge point

$$ 3x^3 + 18x^2 + 27x = 3x(x^2 + 6x + 9) $$

Factor the remaining trinomial of Question 9

Using the Factoring Trinomials and Factoring Polynomials Completely knowledge points

$$ x^2 + 6x + 9 = (x + 3)^2 $$

$$ 3x^3 + 18x^2 + 27x = 3x(x + 3)^2 $$

Factor out the greatest common factor of Question 10

Using the Greatest Common Factor knowledge point

$$ 2c^5 + 44c^4 + 242c^3 = 2c^3(c^2 + 22c + 121) $$

Factor the remaining trinomial of Question 10

Using the Factoring Trinomials and Factoring Polynomials Completely knowledge points

$$ c^2 + 22c + 121 = (c + 11)^2 $$

$$ 2c^5 + 44c^4 + 242c^3 = 2c^3(c + 11)^2 $$

Answer:

Question 9

• (A) \(9x\)
• (B) \(x^3\)
• (C) \(x + 3\) (Correct answer)
• (D) \(x - 3\)

Question 10

• (A) \(2c^3(c + 11)^2\) (Correct answer)
• (B) \(2(c + 11)^2\)
• (C) \(2c^3(c + 11)(c - 11)\)
• (D) \(2c^3(c^2 + 22c + 121)\)