# How do you divide (5x^2+12x-9) /(x^2+3x-10)?

Jul 18, 2016

$\left(5 {x}^{2} + 12 x - 9\right) \div \left({x}^{2} + 3 x - 10\right)$?

=$5 \text{ rem } - 3 x + 41$

#### Explanation:

$\frac{5 {x}^{2} + 12 x - 9}{{x}^{2} + 3 x - 10}$

Before attempting long division or synthetic division, try factoring first

We cannot cancel anything because there are 3 terms on the top and 3 terms on the bottom. We can only cancel if we have factors.

Factorise the numerator and the denominator. Both are quadratic trinomials.

$\frac{\left(5 x - 3\right) \left(x + 3\right)}{\left(x + 5\right) \left(x - 2\right)}$

Oops, there are no factors which can cancel. so we will have to try one of the other methods.

Long division gives the result:

$\left(5 {x}^{2} + 12 x - 9\right) \div \left({x}^{2} + 3 x - 10\right)$?

=$\text{ "5 " rem } - 3 x + 41$