factoring the following polynomial expression completely: 2x^3+x^2-8x-4
To factor the polynomial expression completely, we can use a combination of factoring by grouping and factoring quadratics.
First, let's group the terms in pairs and factor out the greatest common factor from each pair:
(2x^3 + x^2) + (-8x - 4)
Taking out the greatest common factor, we have:
x^2(2x + 1) - 4(2x + 1)
Now, notice that we have a common factor, (2x + 1), in both terms.
Factoring out this common binomial, we get:
(2x + 1)(x^2 - 4)
Next, we can factor the difference of squares within the second parenthesis:
(x + 2)(x - 2)
Therefore, factoring the polynomial expression completely, we have:
(2x + 1)(x + 2)(x - 2)