Question

Which expression is equivalent to (5g^4+5g^3-17g^2+6g)-(3g^4+6g^3-7g^2-12)/g+2

Answer 1

C.

Explanation:

Answer 2

Option C:

`2 g^(3)-5 g^(2)+6`

Solution:

Given expression:

`$(\left(5 g^(4)+5 g^(3)-17 g^(2)+6 g\right)-\left(3 g^(4)+6 g^(3)-7 g^(2)-12\right))/(g+2)`

To find which expression is equal to the given expression.

`$(\left(5 g^(4)+5 g^(3)-17 g^(2)+6 g\right)-\left(3 g^(4)+6 g^(3)-7 g^(2)-12\right))/(g+2)`

Expand the term
`-\left(3 g^(4)+6 g^(3)-7 g^(2)-12\right):-3 g^(4)-6 g^(3)+7 g^(2)+12`

`$=(5 g^(4)+5 g^(3)-17 g^(2)+6 g- 3 g^(4)-6 g^(3)+7 g^(2)+12)/(g+2)`

Arrange the like terms together.

`$=(5 g^(4)- 3 g^(4)+5 g^(3)-6 g^(3)-17 g^(2)+7 g^(2)+6 g+12)/(g+2)`

`$=(2 g^(4)- g^(3)-10 g^(2)+6 g+12)/(g+2)`

Factor the numerator
`2 g^(4)-g^(3)-10 g^(2)+6 g+12=(g+2)\left(2 g^(3)-5 g^(2)+6\right)`

`$=((g+2)\left(2 g^(3)-5 g^(2)+6\right))/(g+2)`

Cancel the common factor g + 2, we get

`=2 g^(3)-5 g^(2)+6`

Hence option C is the correct answer.