Question

question which expression is a factor of both $x^2 - 9$ and $x^2 + 8x + 15$? $\circ$ $(x + 5)$ $\circ$ $(x + 3)$ $\circ$ $(x - 3)$ $\circ$ $(x - 9)$

Explanation:

Step1: Factor \(x^2 - 9\)

Using the difference of squares formula \(a^2 - b^2=(a + b)(a - b)\), where \(a = x\) and \(b = 3\), we get \(x^2 - 9=(x + 3)(x - 3)\).

Step2: Factor \(x^2 + 8x + 15\)

We need to find two numbers that multiply to \(15\) and add up to \(8\). The numbers are \(3\) and \(5\), so \(x^2 + 8x + 15=(x + 3)(x + 5)\).

Step3: Identify common factor

From the factorizations, the common factor of \(x^2 - 9\) and \(x^2 + 8x + 15\) is \((x + 3)\).

Answer:

(x + 3)