Final answer:
To factor completely the expression 4x^2 - 52x + 48, factor out a common factor first and then factor the quadratic trinomial inside the parentheses.
Step-by-step explanation:
To factor completely the expression 4x^2 - 52x + 48, we first look for common factors. In this case, all the coefficients are even, so we can factor out a 4 from each term:
4(x^2 - 13x + 12)
Next, we need to factor the quadratic trinomial inside the parentheses. We look for two numbers that multiply to give 12 and add up to give -13. The numbers -12 and -1 satisfy these conditions, so we can rewrite the quadratic:
4(x - 12)(x - 1)
Therefore, the expression 4x^2 - 52x + 48 factors completely into 4(x - 12)(x - 1).