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

Mar 6, 2016

x + 9

Explanation:

The quotient of a polynomial of degree n, when divided by a polynomial of degree m$\le$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 + $\frac{c}{x - 4} = \frac{{x}^{2} + 5 x + 6}{x - 4}$.
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..