Final answer:
To factor the expression 2x³ + 5x - 8x - 20 completely, use the grouping method and factor out the GCF from each binomial. Then factor out the common binomial.
Step-by-step explanation:
To factor the expression 2x³ + 5x - 8x - 20 completely, we can use the grouping method. First, group the terms so that we have (2x³ + 5x) - (8x + 20). Now factor out the greatest common factor from each binomial. The GCF of 2x³ + 5x is x, and the GCF of -8x - 20 is -4. Factoring out the GCF, we have x(2x² + 5) - 4(2x + 5).
Next, we have two binomials: x(2x² + 5) and -4(2x + 5). Notice that they have a common factor of (2x + 5). Factor out this common binomial to get the factored form: (x - 4)(2x + 5).