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4 votes
Which polynomial is factored completely?

g^5 - g

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

24g^2 - 6g^4

2g2 + 5g + 4

User Paul Swetz
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2 Answers

2 votes
g^5 -g = g(g^4 -1)=g(g^2 -1)(g^2 +1) = g(g-1)(g+1)(g^2 +1)

24g^2 -6g^4 = 6g^2(4 -g^2) = 6g^2(2 -g)(2 +g)
User Nunorbatista
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7.7k points
5 votes

Answer:

The polynomial which is factored completely is
2g^2+5g+4 as these are not further factored.

Explanation:

To find : Which polynomial is factored completely?

Solution :

We factor the given polynomial one by one,

1)
g^5-g


g^5-g=g(g^4-1)


g^5-g=g(g^2-1)(g^2+1)


g^5-g=g(g-1)(g+1)(g^2+1)

2)
4g^3 + 18g^2+20g


4g^3 + 18g^2+20g=2g(2g^(2)+9g+10)


4g^3 + 18g^2+20g=2g(2g^(2)+5g+4g+10)


4g^3 + 18g^2+20g=2g[g(2g+5)+2(2g+5)]


4g^3 + 18g^2+20g=2g(2g+5)(g+2)

3)
24g^2 - 6g^4


24g^2 - 6g^4=6g^(2)(4-g^(2))


24g^2 - 6g^4=6g^(2)(2-g)(2+g)

4)
2g^2+5g+4

This expression is can not be factored with rational number as


D=b^2-4ac\\D=5^2-4(2)(4)\\D=25-32\\D=-7

Discriminant D<0 so there is no rational roots.

So, The polynomial which is factored completely is
2g^2+5g+4 as these are not further factored.

User Busybear
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8.0k points