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

1 Answer
Jul 18, 2016

(5x^2+12x-9) div(x^2+3x-10)?

= 5 " rem " -3x +41

Explanation:

(5x^2+12x-9) /(x^2+3x-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.

[(5x-3)(x+3)]/[(x+5)(x-2)]

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

Long division gives the result:

(5x^2+12x-9) div(x^2+3x-10)?

= " "5 " rem " -3x +41