Use synthetic division to divide the polynomials. $$ \frac{x^{4}-16}{x+2}=\square $$

Question

UpStudy AI · Accepted Answer

To divide the polynomials using synthetic division, we need to follow these steps:

1. Write down the coefficients of the dividend polynomial in descending order of powers of $$ x $$.
2. Write down the root of the divisor polynomial.
3. Perform the synthetic division by multiplying the root with the first coefficient and writing the result below the line.
4. Add the result to the next coefficient and write the result below the line.
5. Repeat steps 3 and 4 until all coefficients have been processed.
6. The result will be the coefficients of the quotient polynomial.

Given the polynomials:
$$ \frac{x^{4}-16}{x+2} $$

The coefficients of the dividend polynomial are: 1, 0, 0, 0, -16 (in descending order of powers of $$ x $$).

The root of the divisor polynomial is -2.

Let's perform the synthetic division:
Calculate the value by following steps:
- step0: Calculate:
  $$1\times 2+0$$
- step1: Calculate:
  $$2+0$$
- step2: Remove 0:
  $$2$$
Performing the synthetic division:

1. Multiply the root (-2) with the first coefficient (1) and write the result below the line: 1 * (-2) = -2
2. Add the result to the next coefficient (0) and write the result below the line: -2 + 0 = -2
3. Multiply the root (-2) with the result (-2) and write the result below the line: -2 * (-2) = 4
4. Add the result to the next coefficient (0) and write the result below the line: 4 + 0 = 4
5. Multiply the root (-2) with the result (4) and write the result below the line: -2 * 4 = -8
6. Add the result to the next coefficient (0) and write the result below the line: -8 + 0 = -8
7. Multiply the root (-2) with the result (-8) and write the result below the line: -2 * (-8) = 16
8. Add the result to the next coefficient (-16) and write the result below the line: 16 + (-16) = 0

The result of the synthetic division is:
$$ x^{3} - 2x^{2} + 4x - 8 $$

Therefore, the quotient polynomial is $$ x^{3} - 2x^{2} + 4x - 8 $$.
The quotient is $$ x^{3} - 2x^{2} + 4x - 8 $$.

Use synthetic division to divide the polynomials.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions