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Answer:
Your answer would be (x + 2)
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Explanation:
The reason why (x + 2) would be the answer is because when you plug "2" in the equation, the final answer would be 0.
In this type of question, we would use the Reminder theorem.
The reminder theorem is a theorem when f(x) could be divisible by (x - a) when the outcome of it is 0. To sum it all up, if you plug in the number and it ends up as 0, that would be a factor.
(x + 2) when you plug "2" in the equation. The two would become a negative since it would be a root number:
In this case, you would pretty much plug the number in and solve.
Work:
(-2)³ + 7(-2)² + 14(-2) + 8
↓
-8 + 7(-2)² + 14(-2) + 8
↓
-8 + 28 + 14(-2) + 8
↓
-8 + 28 + -28 + 8
=
0
After you finish solving, you should get the final answer 0.
(x + 2) would be a factor for x³ + 7x² + 14x + 8
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-Julie