Question

factor the following polynomial.\\(x^3 + 5x^2 + 6x\\)\\(?(x + 2)(x + \square)\\)

Explanation:

Step1: Factor out the GCF

First, identify the greatest common factor (GCF) of the terms \(x^3\), \(5x^2\), and \(6x\). The GCF is \(x\), so we factor it out:
\(x^3 + 5x^2 + 6x = x(x^2 + 5x + 6)\)

Step2: Factor the quadratic

Now, factor the quadratic \(x^2 + 5x + 6\). We need two numbers that multiply to \(6\) and add to \(5\). Those numbers are \(2\) and \(3\), so:
\(x^2 + 5x + 6 = (x + 2)(x + 3)\)

Step3: Combine the factors

Putting it all together, we have:
\(x^3 + 5x^2 + 6x = x(x + 2)(x + 3)\)

Answer:

The first box is \(x\) and the second box is \(3\), so the factored form is \(\boldsymbol{x}(x + 2)(x + \boldsymbol{3})\)