Question

Where did this problem go wrong and how should it have been completed?

Answer 1

Explanation:

Instead of 1, the divider should be -1

-1 ⊥ -3 -4 5 7

3

7

5

_____________

-3 -7 -2 2

So the quotient is -3x^2 - 7x - 2 with a remainder of 5; or

-3x^2 - 7x - 2 + 5/(x-1)

Answer 2

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:

`-3x^2- 7x - 2 + (5)/(x-1)`