Answer:
Problem: They did not add -4 and -3 correctly. The number under -4 and -3 should be -7
Synthetic division
Write the coefficients in the dividend's place and write the zero of the linear factor in the divisor's place:
1 | -3 -4 5 7
Bring the first coefficient down
1 | -3 -4 5 7
-3
Multiply it with the divisor (-3 x 1) and write it below the next coefficient:
1 | -3 -4 5 7
-3
-3
Add them (-4 + -3) and write the value below:
1 | -3 -4 5 7
-3
-3 -7
Repeat. Multiply -7 with the divisor, write it below the next coefficient:
1 | -3 -4 5 7
-3 -7
-3 -7
Add:
1 | -3 -4 5 7
-3 -7
-3 -7 -2
Repeat. Multiply -2 with the divisor, write it below the next coefficient then add. The last term is the remainder
1 | -3 -4 5 7
-3 -7 -2
-3 -7 -2 | 5 → R
Therefore, the solution is:
[tex]-3x^2- 7x - 2 + \dfrac{5}{x-1}[/tex]
