Question

How do you find the quotient of x^2+5x+6 / x-4?

Answer 1

x + 9

Explanation:

The quotient of a polynomial of degree n, when divided by a polynomial of degree m`<=`n, is a polynomial of degree `n-m`..
The remainder is a polynomial of degree m`-`1.
Here, n = 2 and m = 1.
So, a x + b + `c/(x-4)=(x^2+5x+6)/(x-4)`.
To get a, b and c, multiply both sides by `x-4` and compare coefficients of like terms.
The quotient is x + 9 and the remainder is 42..