Answer: [tex]2x^2+3x-2[/tex]
Step-by-step explanation:
You can do long division, which is very very hard to show with typing on a keyboard. You essentially want to divide the leading coefficient for each term. Ill try my best to explain it.
Do [tex]\frac{2x^3}{x}=2x^2[/tex]. Write 2x^2 down. Now multiply (x - 3) by it. Then subtract it from the trinomial.
[tex]2x^2*(x-3)=2x^3 -6x^2\\(2x^3 -3x^2-11x+6)-(2x^3-6x^2) = 3x^2-11x+6[/tex]
Now do [tex]\frac{3x^2}{x} =3x[/tex]. Write that down next to your 2x^2. Multiply 3x by (x - 3) to get:
[tex]3x(x-3)=3x^2-9x\\(3x^2-11x+6)-(3x^2-9x)=-2x+6[/tex]
Your final step is to do [tex]\frac{-2x}{x} =-2[/tex]. Write this -2 next to your other two parts
Multiply -2 by (x - 3) to get:
[tex]-2(x-3)=-2x+6\\(-2x+6)-(-2x+6)=0[/tex]
Our remainder is 0 so that means (x - 3) goes into that trinomial exactly:
[tex]2x^2+3x-2[/tex] times
