Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping?

x (x2 + 4) + 5 (x2 + 4)

x? (x + 4) + 5 (x + 4) ►

x2 (x + 5) + 4 (x + 5)

x (x2 + 5) + 4x (x2 + 5)

The answer to your question is x² (x + 4) + 5 (x + 4) second choice (chance?)

Step-by-step explanation:

Factor by grouping

x³ + 4x² + 5x + 20

Let's group the first two terms and the second two terms

(x³ + 4x²) + (5x + 20)

The Greatest common factor of the first group is "x²" and the GCF of the second group is "5".

x² (x + 4) + 5 (x + 4)

Comparing with the choices, I think the right answer is the second one but it is not "?" but 2.

Second choice x² (x + 4) + 5 (x + 4)

Step-by-step explanation:

To factor this way, first our terms need a common factor to pull out. So the two parenthesized parts must be the same, as they are in all the choices.

Next the expression actually has to be correct. The first one gets a 4x term, so that's wrong. The third gets a 4x as well, wrong. The fourth gets a 0x², not that one either. That leaves the second.

The second has a? where there should be a squared; let's assume that's a typo. It expands to

x² (x + 4) + 5 (x + 4) = x³ + 4x² + 5x + 20

which is correct and it factors as

(x² + 5) (x + 4)