How do you divide $\frac{5 x^{2} + 12 x - 9}{x^{2} + 3 x - 10}$ $(5x^2+12x-9) /(x^2+3x-10)$ ?

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Answer 1 · 2016-07-18T21:44:11

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

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

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

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.

$\frac{(5 x - 3) (x + 3)}{(x + 5) (x - 2)}$ $[(5x-3)(x+3)]/[(x+5)(x-2)]$

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

Long division gives the result:

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

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

How do you divide (5x^2+12x-9) /(x^2+3x-10)5x2+12x−9x2+3x−10(5x^2+12x-9) /(x^2+3x-10)?