Factor out the greatest common factor. If the greatest common factor is 1,just retype the polynomial. 2c^3+8c^2 square

## Step 1<br />The problem asks us to factor out the greatest common factor (GCF) from the given polynomial \(2c^{3}+8c^{2}\). The GCF is the largest number or term that can be divided evenly into all terms of the polynomial.<br /><br />## Step 2<br />To find the GCF, we need to look at each term of the polynomial and identify the largest number or term that can be divided evenly into all terms. In this case, the GCF is \(2c^{2}\), as it is the largest term that can be divided evenly into both \(2c^{3}\) and \(8c^{2}\).<br /><br />## Step 3<br />Once we have identified the GCF, we can factor it out of the polynomial. This means we divide each term of the polynomial by the GCF and write the polynomial as the GCF times the resulting terms.<br /><br />## Step 4<br />So, we divide \(2c^{3}\) by \(2c^{2}\) to get \(c\), and \(8c^{2}\) by \(2c^{2}\) to get \(4\).<br /><br />## Step 5<br />Therefore, the factored form of the polynomial \(2c^{3}+8c^{2}\) is \(2c^{2}(c+4)\).