Question

drag each term to the correct location on the expression. each term can be used more than once, but not all term
what is the completely factored form of the quadratic expression $3x^2 - 30x - 72$?
1 x 4 3 6 3x $x^2$ 12
$\square(x - \square)(\square + 2)$
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Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(3x^2\), \(-30x\), and \(-72\). The GCF of 3, 30, and 72 is 3. So we factor out 3 from the quadratic expression:
\(3x^2 - 30x - 72 = 3(x^2 - 10x - 24)\)

Step2: Factor the quadratic inside the parentheses

Now, we need to factor the quadratic \(x^2 - 10x - 24\). We look for two numbers that multiply to \(-24\) and add up to \(-10\). The numbers are \(-12\) and \(2\) because \(-12 \times 2 = -24\) and \(-12 + 2 = -10\). So we can factor \(x^2 - 10x - 24\) as \((x - 12)(x + 2)\).

Step3: Combine the factors

Putting it all together, the completely factored form of \(3x^2 - 30x - 72\) is \(3(x - 12)(x + 2)\).

Answer:

The first box is \(3\), the second box is \(12\), and the third box is \(x\). So the filled expression is \(3(x - 12)(x + 2)\).