Which polynomial is factored completely?
g^5-g
4g^3+18g^2+20g
24g^2-6g^4
2g^2+5g+4

Option (4)

Step-by-step explanation:

To solve this question we will try to factor the expressions given in each option.

Option (1)

g⁵ - g = g(g⁴ - 1)

         = g(g² - 1)(g² + 1)

         = g(g - 1)(g + 1)(g² + 1)

Option (2)

4g³ + 18g² + 20g = 2g(2g² + 9g + 10)

                            = 2g[2g + 5g + 4g + 10]

                            = 2g[g(2g + 5) + 2(g + 5)]

                            = 2g(2g + 5)(g + 2)

Option (3)

24g² - 6g⁴ = 6g²(4 - g²)

                 = 6g²(2 - g)(2 + g)

Option (4)

2g² + 5g + 4

This expression is the in the completely factored form.

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