Answer:
Step-by-step explanation:
The best way to do this is to subtract the 2x-3 from the polynomial to find the difference. The difference is what needs to be added to the polynomial to get 2x-3 as the sum.
5x² - 3x - 9 - (2x - 3) =
5x² - 3x - 9 - 2x + 3 =
5x² - 5x - 6
This should be what we need to add to the polynomial given to give us a sum of 2x - 3. But if we add 5x² to another 5x² we get 10x². We want to eliminate the x²-ed terms altogether, so let's take the opposite of our sum and see what happens when we add. The opposite of our sum is
-5x² + 5x + 6. Now let's add:
-5x² + 5x + 6 + 5x² - 3x - 9 =
2x - 3. Therefore, the polynomial to add in is
-5x² + 5x + 6
