Question

question 3 (multiple choice worth 1 points)
(02.01r)

factor completely \\(49x^2 - 81\\).

• \\((7x + 9)^2\\)
• \\((7x - 9)^2\\)
• \\((7x + 9)(7x - 9)\\)
• \\(7x - 9\\)

question 4 (multiple choice worth 1 points)
(02.01r mc)

one of the factors of \\(6x^3 - 864x\\) is

• \\(4\\)
• \\(x^2\\)
• \\(x + 12\\)
• \\(x - 8\\)

Explanation:

Identify perfect squares

Identify terms as squares.

$$ 49x^2 = (7x)^2,\quad 81 = 9^2 $$

Apply difference of squares

Factor the expression.

$$ a^2 - b^2 = (a + b)(a - b) $$

$$ 49x^2 - 81 = (7x + 9)(7x - 9) $$

Extract greatest common factor

Using the Greatest Common Factor knowledge point, factor out the common term.

$$ 6x^3 - 864x = 6x(x^2 - 144) $$

Factor the remaining binomial

Identify and factor the difference of squares.

$$ x^2 - 144 = x^2 - 12^2 = (x + 12)(x - 12) $$

$$ 6x^3 - 864x = 6x(x + 12)(x - 12) $$

Identify the correct factor

Compare factors with options.
The factors are \(6\), \(x\), \((x + 12)\), and \((x - 12)\).
The matching option is \(x + 12\).

Answer:

Question 3

• (A) \((7x + 9)^2\)
• (B) \((7x - 9)^2\)
• (C) \((7x + 9)(7x - 9)\) (Correct answer)
• (D) \(7x - 9\)

Question 4

• (A) \(4\)
• (B) \(x^2\)
• (C) \(x + 12\) (Correct answer)
• (D) \(x - 8\)