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

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Answer 1 · 2016-07-18T21:44:11

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

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

#(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#