Questions: Factor completely. 5 w^2 + 60 w + 100

Factor completely. 5 w^2 + 60 w + 100
Transcript text: Factor completely. \[ 5 w^{2}+60 w+100 \]
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Solution

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Solution Steps

To factor the quadratic expression completely, we first look for a common factor in all the terms. Then, we apply the quadratic formula or factor by grouping if necessary to further simplify the expression.

Step 1: Identify the Expression

We start with the quadratic expression: \[ 5w^2 + 60w + 100 \]

Step 2: Factor Out the Greatest Common Factor

The greatest common factor (GCF) of the terms \(5w^2\), \(60w\), and \(100\) is \(5\). We factor this out: \[ 5(w^2 + 12w + 20) \]

Step 3: Factor the Quadratic Expression

Next, we need to factor the quadratic expression \(w^2 + 12w + 20\). We look for two numbers that multiply to \(20\) and add to \(12\). These numbers are \(2\) and \(10\). Thus, we can factor the quadratic as: \[ w^2 + 12w + 20 = (w + 2)(w + 10) \]

Step 4: Combine the Factors

Combining the factors, we have: \[ 5(w + 2)(w + 10) \]

Final Answer

The completely factored form of the expression is: \[ \boxed{5(w + 2)(w + 10)} \]

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