What algebraic expression must be added to the sum of 3x2 + 4x+8 and 2x2-6x+3 to give 9x2-2x-5 as the result?

4x² - 16 is the algebraic expression that must be added to get the result as 9x² - 2x - 5.

Step-by-step explanation:

The question is asked for the algebraic expression must be added to the sum of 3x²+4x+8 and 2x2-6x+3 to give 9x² - 2x - 5 as the result.

Therefore,

The first step is to find of sum of 3x²+4x+8 and 2x²-6x+3.

To find the sum:

3x²+4x+8

2x²-6x+3

5x²-2x+11

The sum is 5x²-2x+11.

Now, the second step is to subtract 5x²-2x+11 from the result 9x² - 2x - 5.

9x² - 2x - 5

- (5x²-2x+11)

4x² - 16

Thus, 4x²-16 is the algebraic expression that must be added with 5x²-2x+11 to get a result of 9x² - 2x - 5.