The easiest way to solve this is to do the long division. The solution is show below:
2x² - 8x - 3
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x+ 4 |2x³ - 35 x -12
- 2x³ + 8x²
------------------
-8x² - 35x
- -8x² - 32x
-----------------
-3x - 12
- -3x - 12
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0
This is how it's done step by step. First, find a quotient that could divide the first term of the equation 2x³ - 35 x -12. So, that would be 2x² because 2x² (x+4) = 2x³ + 8x². Next, you subtract this product from the original equation. 2x³ will be cancelled out leaving -8x². So, let's move onto the next term by carrying it down. So, we carry -35x down.Now, it becomes -8x²-35x. The same procedure follows. We find a quotient that can divide the first terms which is -8x². So, that would be -8x because -8x(x+4) = -8x²-32x. Subtract again, we get -3x. Carry down the next term which is -12. Lastly, the last term of the quotient is -3 because -3(x+4) = -3x-12 which cancels out the whole equation.
Therefore, the quotient is 2x²-8x-3.