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What should be added to [tex]2x^3 + 6x^2 - 5x + 8[/tex] to get [tex]3x^3 - 2x^2 + 6x + 15[/tex]?

A. [tex]x^3 + 8x^2 + 10x + 7[/tex]
B. [tex]x^3 - 4x^2 + 11x + 7[/tex]
C. [tex]x^3 - 6x^2 + 11x + 7[/tex]
D. [tex]x^3 + 6x^2 + 11x + 7[/tex]

Answer :

Final answer:

The polynomial x^3 - 8x^2 + 11x + 7 must be added to 2x^3 + 6x^2 - 5x + 8 to get 3x^3 - 2x^2 + 6x + 15.

Explanation:

In order to find out what should be added to 2x^3 + 6x^2 - 5x + 8 to get 3x^3 - 2x^2 + 6x + 15, we can subtract the first polynomial from the second one. This will give us the difference between the two, which is what we must add to the first polynomial to get the second one.

So, we perform 3x^3 - 2x^2 + 6x + 15 - (2x^3 + 6x^2 - 5x + 8). This simplifies to x^3 - 8x^2 + 11x + 7.

By examining the answer choices, we can see that the result matches with option (b) x^3 - 8x^2 + 11x + 7. So, this is the correct answer.

Learn more about Polynomial Addition here:

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