Question

7.6 advanced factoring methods quiz

true or false:

difference of squares works for addition problems like \\(x^2+16\\)

true

false

Explanation:

Analyze the algebraic structure

Using the Factoring Polynomials knowledge point

$$ x^2 + 16 = x^2 + 4^2 $$

Evaluate the difference of squares rule

Using the Factoring Polynomials knowledge point

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

The expression \(x^2 + 16\) is a sum of squares, not a difference of squares. Over the real numbers, a sum of squares cannot be factored into linear binomials. Therefore, the difference of squares method does not work for addition problems like \(x^2 + 16\).

Answer:

• True
• (B) False (Correct answer)