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.