Question

Please help on this one ?

Answer 1

The Synthetic Division form of Given Division Problem is :

✿
`-5\;\arrowvert\overline{\;4\;\;\;\;\;-13\;\;\;\;\;\;8}`

Option C is the Answer

Answer 2

In synthetic division for
`\( (4x^2 - 13x + 8)/(x + 5) \)`, option C (-5 | 4 -13 8) correctly represents the coefficients, showcasing the division process with a remainder of 8.

The synthetic division problem given is
`\( (4x^2 - 13x + 8)/(x + 5) \)`. Synthetic division is a method used to divide polynomials, particularly when dividing by a linear factor of the form (x - c) . The correct representation in synthetic division form would be:

**C. -------------

- 5 | 4 - 13 8**

Here's the breakdown of the synthetic division:

1. The divisor x + 5 corresponds to c = -5, so the root is x = -5.

2. Write down the coefficients of the dividend 4x^2 - 13x + 8 in the synthetic division box.

3. Bring down the leading coefficient, which is 4 in this case.

4. Multiply the root (-5) by the leading coefficient (4) and write the result below the second column. Add the result to the second column.

5. Multiply the root by the result from step 4 and write the result below the third column. Add the result to the third column.

The final result in the bottom row represents the coefficients of the quotient, and the last number (8) is the remainder. The synthetic division in option C accurately reflects this process.