Find a polynomial, which, when added to the polynomial 5x2–3x–9, is equivalent to: 0
Huh? The original polynomial?
You want
(5x^2-3x-9)-(5x^2-3x-9) = 0
now just change the signs of the 2nd polynomial so you can add it instead of subtracting.
well,
5 + -5 = 0
-3 + 3 = 0
...
5x^2-3x-9
To find the polynomial that, when added to the given polynomial, results in 0, we need to solve the equation:
(5x^2 - 3x - 9) + P(x) = 0
Here, P(x) represents the polynomial we are trying to find.
To solve the equation, we can rearrange it to isolate P(x):
P(x) = - (5x^2 - 3x - 9)
To simplify this expression, we distribute the negative sign:
P(x) = -5x^2 + 3x + 9
Therefore, the polynomial we are looking for is -5x^2 + 3x + 9.