To factor the expression 5x² – 40 completely, we start by looking for common factors in the terms. The coefficients are 5 and -40, so the greatest common factor (GCF) is 5.
We can factor out 5 from the expression:
5(x² – 8).
Now, we need to factor the expression inside the parentheses. The expression x² – 8 is a difference of squares, which can be factored further. We recognize that 8 can be expressed as the square of 2√2, allowing us to write:
x² – (2√2)².
Using the difference of squares formula, a² – b² = (a – b)(a + b), we apply it here:
5(x – 2√2)(x + 2√2).
Thus, the completely factored form of the original expression 5x² – 40 is:
5(x – 2√2)(x + 2√2).