Question

factor: (greatest coefficient first. if coefficients are the same, least valued constant first.)
$2x^2 + 22x + 60$
$= a (bx + c) (dx + e)$.
$= \square (\square x + \square)(\square x + \square)$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(2x^2\), \(22x\), and \(60\). The GCF of 2, 22, and 60 is 2. So we factor out 2:
\(2x^2 + 22x + 60 = 2(x^2 + 11x + 30)\)

Step2: Factor the quadratic

Now factor the quadratic \(x^2 + 11x + 30\). We need two numbers that multiply to 30 and add up to 11. Those numbers are 5 and 6. So:
\(x^2 + 11x + 30 = (x + 5)(x + 6)\)

Step3: Combine the factors

Putting it all together, the factored form is:
\(2x^2 + 22x + 60 = 2(x + 5)(x + 6)\)

Answer:

\(2\) \((1x + 5)\) \((1x + 6)\) (or simply \(2(x + 5)(x + 6)\) with the boxes filled as \(2\), \(1\), \(5\), \(1\), \(6\))