Factor completely 4x^2-48x-52

To factor the quadratic expression completely, we can first look for common factors of all the terms:

4x^2 - 48x - 52

The greatest common factor of the coefficients is 4. Therefore, we can factor it out:

4(x^2 - 12x - 13)

Now, we need to factor the quadratic trinomial inside the parentheses. We want to find two numbers whose product is -13 and whose sum is -12. The factors of -13 are -1 and 13, and since we need a sum of -12, we can use -13 and 1. Rewriting the middle term:

4(x^2 - 13x + x - 13)

Next, we group the terms:

4((x^2 - 13x) + (x - 13))

Now, we can factor out the common factor from each group:

4(x(x - 13) + 1(x - 13))

Notice that we have a common binomial factor of (x - 13) in both terms. We can factor it out:

4(x - 13)(x + 1)

Therefore, the fully factored form of 4x^2 - 48x - 52 is 4(x - 13)(x + 1).