Use synthetic division to divide $2x^3+6x^2-11x-12$ by $x+4$ I get $2x^2+14x+45+\frac{168}{x+4}$ whereas textbook solution says $2x^2-2x-3$

algebra-precalculus

I would normally use markup to layout my question but with synthetic division I don't know how to lay it out with markup, so I will post a screen shot.

Question is in the title. I am working on exercise number 23 here. Divide $2x^3+6x^2-11x-12$ by $x+4$ using synthetic division. I got $2x^2+14x+45+\frac{168}{x+4}$ whereas the textbook solution here is $2x^2-2x-3$.

Here is my working (sorry for giving you a sore neck):
enter image description here

Where did I go wrong and how can I arrive at $2x^2-2x-3$?

Best Answer

The root is $x = -4$. So you have to take $-4$ instead of $4$

enter image description here

Hence you have $2x^2-2x-3$

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