The complete factoring of the expression 5x^2 - 40x is 5x(x - 8), where 5x is the greatest common factor.
The student is asking to complete the factoring of the quadratic expression 5x^2 - 40x. To factor this expression, you want to find the greatest common factor (GCF) that can be factored out of both terms. In this case, the GCF is 5x. When we factor out 5x from each term of the expression, we divide each term by 5x.
Here's the step-by-step process:
Identify the GCF of 5x^2 and -40x, which is 5x.
Divide each term by the GCF: 5x^2 divided by 5x equals x, and -40x divided by 5x equals -8.
Write the original expression as the product of the GCF and the resulting terms: 5x(x - 8).
So, the completed factoring of 5x^2 - 40x is 5x(x - 8).