Here, we want to factor the given polynomial
The easiest way to go about this is to factor out the highest common factor which is 4 in this case
Thus, we have;
[tex]4x^2-8x-60=4(x^2-2x-15)[/tex]So, we can proceed to factor what we have in the bracket
We can do this by finding two factors which when added gives -2x and when multiplied will give -15x^2
Thus, we have;
[tex]\begin{gathered} x^2-2x-15=x^2-5x+3x-15 \\ =\text{ x(x-5)+3(x-5)} \\ =\text{ (x+3)(x-5)} \end{gathered}[/tex]From here, we proceed to replace the 4 we removed and we get the initial polynomial
Hence;
[tex]4x^2-8x-60\text{ = 4(x-5)(x+3)}[/tex]