Question

ve for all values of x by factoring.

x² - 8x + 15 = 0

answer attempt 1 out of 2

Explanation:

Step1: Factor the quadratic

We need two numbers that multiply to \(15\) and add to \(-8\). The numbers are \(-3\) and \(-5\) since \((-3)\times(-5) = 15\) and \(-3 + (-5)=-8\). So, \(x^{2}-8x + 15=(x - 3)(x - 5)\).

Step2: Solve for \(x\)

Set each factor equal to zero:

• For \(x - 3=0\), we get \(x = 3\).
• For \(x - 5=0\), we get \(x = 5\).

Answer:

\(x = 3\) or \(x = 5\)