Factor completely. If not factorable, write Prime. 8z^2-44z+60=square

## Step 1<br />The given expression is \(8z^{2}-44z+60\). We need to factorize this expression. Factoring is a process where we break down the expression into simpler terms that, when multiplied, give the original expression.<br /><br />## Step 2<br />To factorize the given expression, we need to find two numbers that multiply to \(8*60=480\) (the product of the coefficient of \(z^{2}\) and the constant term) and add up to \(-44\) (the coefficient of \(z\)).<br /><br />## Step 3<br />The numbers that satisfy these conditions are \(-20\) and \(-24\), because \(-20*-24=480\) and \(-20-24=-44\).<br /><br />## Step 4<br />We can then rewrite the middle term of the expression as \(-20z-24z\), giving us \(8z^{2}-20z-24z+60\).<br /><br />## Step 5<br />Next, we group the terms and factor by grouping. This gives us \(4z(2z-5)-12(2z-5)\).<br /><br />## Step 6<br />Finally, we factor out the common binomial term \((2z-5)\), giving us \((4z-12)(2z-5)\).