Question

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

Answer 1

Clearly, quotient =`-(x^2+3x+6),` and, remainder = `-35`.

Explanation:

Numerator `=-x^3+color(red)2x^2+color(blue)9xcolor(green)(-5)= -x^3+color(red)5x^2color(red)(-3)x^2+color(blue)15xcolor(blue)(-6)xcolor(green)(+30-35)=-x^2(x-5)-3x(x-5)-6(x-5)-35=(x-5)(-x^2-3x-6)-35.`

Hence, the given rational function `={(x-5)(-x^2-3x-6)-35}/(x-5)={-(x-5)(x^2+3x+6)/((x-5))}-(35}/(x-5).`

Clearly, quotient =`-(x^2+3x+6),` and, remainder = `-35`.