Question

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

Answer 1

Option C:

$2 g^{3}-5 g^{2}+6$

Solution:

Given expression:

$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}$

To find which expression is equal to the given expression.

$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}$

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

         $=\frac{5 g^{4}+5 g^{3}-17 g^{2}+6 g- 3 g^{4}-6 g^{3}+7 g^{2}+12}{g+2}$

Arrange the like terms together.

         $=\frac{5 g^{4}- 3 g^{4}+5 g^{3}-6 g^{3}-17 g^{2}+7 g^{2}+6 g+12}{g+2}$

         $=\frac{2 g^{4}- g^{3}-10 g^{2}+6 g+12}{g+2}$

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

         $=\frac{(g+2)\left(2 g^{3}-5 g^{2}+6\right)}{g+2}$

Cancel the common factor g + 2, we get

         $=2 g^{3}-5 g^{2}+6$

Hence option C is the correct answer.

Answer 2

Answer:

C.

Step-by-step explanation: