Questions: -4w^2+36w-72

Transcript text: -4 w^{2}+36 w-72

Solution

Solution Steps

Step 1: Write the Polynomial

We start with the polynomial expression: \[ -4 w^{2} + 36 w - 72 \]

Step 2: Factor Out the Greatest Common Factor

Identify the greatest common factor (GCF) of the coefficients \(-4\), \(36\), and \(-72\). The GCF is \(-4\). We factor this out: \[ -4 \left( w^{2} - 9w + 18 \right) \]

Step 3: Factor the Quadratic Expression

Next, we need to factor the quadratic expression \(w^{2} - 9w + 18\). We look for two numbers that multiply to \(18\) (the constant term) and add to \(-9\) (the coefficient of \(w\)). The numbers \(-6\) and \(-3\) satisfy these conditions. Thus, we can factor the quadratic as: \[ -4 \left( w - 6 \right) \left( w - 3 \right) \]

Step 4: Write the Fully Factorized Form

The fully factorized form of the original polynomial is: \[ -4 \left( w - 6 \right) \left( w - 3 \right) \]