Question

Use synthetic divison
please show the work

Answer 1

The result of the division
`\( (x^5 - 6x^4 + 9x^3 + 6x - 20) / (x - 2) \)` is
`\( x^4 - 8x^3 + 2x^2 + 4 \)`, with no remainder.

Synthetic division is a method used to divide a polynomial by a linear factor of the form (x - c). In this case, we want to divide
`\(x^5 - 6x^4 + 9x^3 + 6x - 20\)` by
`\(x - 2\)`.

Here's the synthetic division step by step:

2 | 1 -6 9 0 6 -20

1. Bring down the leading coefficient, which is 1:

2 | 1

2. Multiply the divisor (2) by the current result and write the product under the next coefficient:

2 | 1 -6

--------

2

3. Add the next coefficient (9) to the result:

2 | 1 -6 9

--------

2 6

4. Repeat the process until you reach the end of the polynomial:

2 | 1 -6 9 0 6

---------------------

2 -8 2 4

The final row represents the coefficients of the quotient polynomial. So, the result of the division is
`\(x^4 - 8x^3 + 2x^2 + 4\)`, and the remainder is 0.

Therefore,
`\( (x^5 - 6x^4 + 9x^3 + 6x - 20) / (x - 2) = x^4 - 8x^3 + 2x^2 + 4 \)`.