Answer:
2x + 3
Step-by-step explanation:
So, the equation here is:
[tex]\frac{2x^2 - 5x - 12}{x - 4}[/tex]
And so, using this we can set up our synthetic equation using the dividends as the coefficients of the equation, which are 2, -5, and -12; and the divisor 4, which derives from -4.
It's a bit hard to create a table here, so I'll just write out the values and hope you piece it together.
4 | 2 -5 -12
| 2 8 12
2 3 0
Thus, we are given our coefficients for our desired equation.
2x + 3
And we can ascertain this to be the answer by working the converse.
(2x + 3)(x - 4)
2x² - 5x - 12
