Find a polynomial, which, when added to the polynomial 5x^2-3x-9, is equivalent to

x^2-5x+6

So this is easy counting

so 5x^2-3x-9

we have 5 x^2's

-3 x's

-9

wat do we add to that to get

1 x^2's

-5 x's

+6

so we do each

5x^2+what=1x^2

subtract 5x^2

from both sides

what=-4x^2

first is - 4x^2

then we have - 3x to - 5x

-3x+what=-5x

add 3x to both sides

what=-2x

second is - 2x

-9 to 6

-9 + what=6

ad d9

what=15

last is 15

thereffor add - 4x^2-2x+15