Question

factor:
e² - 8e + 15
options:
(e - 5)(e - 3)
(e + 5)(e + 3)
(e + 15)(e - 1)
(e - 7)(e - 8)

Explanation:

Step1: Identify the form

We have a quadratic trinomial of the form \(x^2 + bx + c\) (here \(x = e\), \(b=-8\), \(c = 15\)). We need two numbers that multiply to \(c\) (15) and add up to \(b\) (-8).

Step2: Find the numbers

We find two numbers: -5 and -3. Because \((-5)\times(-3)=15\) and \((-5)+(-3)=-8\).

Step3: Factor the trinomial

Using the formula \(x^2+bx + c=(x + m)(x + n)\) where \(m\) and \(n\) are the two numbers we found, we get \(e^2-8e + 15=(e-5)(e - 3)\).

Answer:

\((e - 5)(e - 3)\) (corresponding to the first option: (e - 5)(e - 3))