Question

What must be added to 5x³ − 2x² + 6x + 7 to make the sum x³ + 3x² − x + 1?

Answer 1

Let the expression be added be X.
(5x³ − 2x² + 6x + 7)+X = (x³ + 3x² − x + 1)
X = (x³ + 3x² − x + 1) - (5x³ − 2x² + 6x + 7)
Changing the sign of each term of the expression that is to be subtracted and then adding:
X = (x³ + 3x² − x + 1) + (-5x³ + 2x² - 6x - 7)
X = x³ + 3x² − x + 1-5x³ + 2x² - 6x - 7

Rearranging and collecting the like terms:
X = (1-5)x³ + (3+2)x² +(−1-6) x + 1-7
X = -4x³ + 5x² − 7x -6

So, -4x³ + 5x² − 7x -6 must be added to 5x³ − 2x² + 6x + 7 to get the sum as x³ + 3x² − x + 1.