Question

what should be subtracted from x3 + 7x2 + 6x - 10 so that resulting polynomial is exactly divisible by x2 + 2x - 3

Answer 1

By dividing, we get
$\frac{x^3+7x^2+6x-10}{x^2 + 2x-3}$ = $x+5$ (as the quotient)
(and $-x+5$ as remainder)

Therefore, ($x^3+7x^2+6x-10$) - ($-x+5$) will be exactly divisible by $x^2 + 2x-3$
which is $X^3+7x^2+7x-15$