Question

How do you divide `(2x^3+ 4 x^2+4x+12)/(x-7)`?

Answer 1

Here it is again because somebody deleted it

Explanation:

Using Synthetic Division it would look something like this.
In order to divide this, you can use Synthetic Division. Take the negative of your bottom constant, or the negative of -7, which is 7. Then write out all of your leading coefficients. It should look like this:

7 I ) 2 4 4 12
I
I____

Now, bring the first 2 down.

7 I) 2 4 4 12
I
I____
2

Multiply the 7 by the 2 and put your answer under the 4

7 I ) 2 4 4 12
I 14
I____
2

Now add 4 and 14 and put that number underneath them.

7 I) 2 4 4 12
I 14
I____
2 18

Multiply the 7 by the 18 and put that under the 4

7 I) 2 4 4 12
I 14 126
I____
2 18

Add the 4 and the 126 (I'm hoping you're starting to see a pattern here)!

7 I) 2 4 4 12
I 14 126
I____
2 18 130

Multiply the 7 and the 130 and put it under the 12 then add them

7 I) 2 4 4 12
I 14 126 910
I____
2 18 130 922

Now you essentially have your equation. The bottom row of numbers are your new coefficients in your new equation. However your new highest exponent is one less than your original equation because you divided an x out of it.

Your equation is:

2x^2+18x+130 and a remainder of 922/x-7. An easier way to write the remainder is r(922) (This implies that it is put over x-7). I know the formatting on here is wierd so if this didn't make sense Khan Academy has a great video on this:Synthetic Division

Hope this helps!