Question

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

Answer 1

3x^2 + 4x + 8 + 2x^2 - 6x + 3 to give result as 9x^2 -2x - 5


3x^2 + 4x + 8 + 2x^2 - 6x + 3 
= 5x^2 - 2x + 11

so

9x^2 -2x - 5 - (5x^2 - 2x + 11)
= 9x^2 -2x - 5 -  5x^2 +  2x - 11
= 4x^2 -16

answer

expression (4x^2 -16) must be added to the sum of (3x^2 + 4x + 8) and (2x^2 - 6x + 3) to give the result as (9x^2 - 2x - 5)