Question

Which polynomial is factored completely?

A. g^5 -g

B. 4g^3+18g^2+20g

C. 24g^2-6g^4

D. 2g^2+5g+4

Answer 1

Polynomial
D
all terms are different

Answer 2

Option D. is the correct option.

Explanation:

We will factorize each polynomial given in the question.

A.
`g^(5)-g=g(g^(4)-1)=g(g^(2)-1)(g^(2)+1)=g(g-1)(g+1)(g^(2)+1)`

B.
`4g^(3)+18g^(2)+20g=2g(2g^(2)+9g+10)=2g(2g^(2)+5g+4g+10)`

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

C.
`24g^(2)-6g^(4)=6g^(2)(4-g^(2))=6g^(2)(2-g)(2+g)`

D.
`2g^(2)+5g+4` is factored completely.

Therefore answer is option D.