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3 years ago

What comes next!T,F,S,S,M

Mathematics

1 answer:

Wittaler [7]3 years ago

6 0

Answer:

E,D

Step-by-step explanation:

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Option C:

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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}$

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$$=\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.

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