3x^3 +2x + 5
Did you mean (3x^4+ 6x^3 + 2x^2 +9x + 10)/(x+2)?
First let’s set up a synthetic division template. We’re dividing by (x+2), which is in the form (x+c). What goes on the outside of the template is -c, so -2 is on the outside.
Then, let’s write down all the coefficients of the terms in the quantity being divided, (3x^4 +6x^3+ 2x^2+ 9x +10). Inside the template we have 3, 6, 2, 9, and 10 because we write down the coefficients in order of how high their powers are.
Then we bring down the first coefficient to the bottom of the template. And now we multiply 3 and -2, which gives us -6. Write -6 under the second term of the dividend, which is 6. Now add. We get 0. We repeat this cycle of multiplying and adding.
0 times -2 is zero. Now the third term of the dividend, 2, plus 0 is 2.
-2 times 2 is -4. The fourth term of the dividend, 9, plus -4 is 5.
5 times -2 is -10. 10 plus -10 is zero, and so our remainder is zero.
Now rewrite the numbers on the bottom of the template as our quotient. We have 3, 0, 2, and 5, on the bottom (we can ignore the remainder because it’s zero). Every coefficient gets written with x to one power lower than the original dividend.
So we can write 3x^3 + 0x^2 + 2x + 5.
Rewrite as 3x^3 + 2x + 5.
