Question

factor: (greatest coefficient first. if coefficients are the same, least valued constant first.)
$x^2 + 6x + 8$
$= a (bx + c) (dx + e)$
$= \square (\square x + \square )(\square x + \square )$

Explanation:

Step1: Identify the form

The quadratic is \(x^2 + 6x + 8\), so \(a = 1\) (leading coefficient).

Step2: Find two numbers

Find two numbers that multiply to \(8\) (constant term) and add to \(6\) (coefficient of \(x\)). The numbers are \(2\) and \(4\) (since \(2\times4 = 8\) and \(2 + 4 = 6\)).

Step3: Factor the quadratic

Using the numbers, we factor as \((x + 2)(x + 4)\). So \(a = 1\), \(b = 1\), \(c = 2\), \(d = 1\), \(e = 4\).

Answer:

\(1\) (\(1x + 2\))(\(1x + 4\))