Question

Divide the following polynomials using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x4 + 81) (x + 3)

Answer 1

To divide the given polynomials using synthetic division, we identify the zero associated with the divisor, set up the synthetic division process, and perform operations to find the quotient which is x^3 - 3x^2 + 9x - 27 without any remainder.

Step-by-step explanation:

To divide the polynomials x^4 + 81 by x + 3 using synthetic division, we first identify the zero of the divisor (x + 3), which is x = -3. We then set up the synthetic division as follows:

• Write down the coefficients of the dividend, which in this case are 1 (for x^4), 0 (for x^3), 0 (for x^2), 0 (for x), and 81 (constant term).
• Bring down the leading coefficient (1) to the bottom row.
• Multiply the divisor's zero (-3) by the number just written below the line and place the result in the next column of the second row.
• Add the numbers in the second column and write the result below the line. Repeat the multiplication and addition steps until all columns are filled.
• The numbers in the bottom row represent the coefficients of the quotient polynomial.

The synthetic division would look like this:

-3 | 1 0 0 0 81
| -3 9 -27 81
------------------
1 -3 9 -27 0

The quotient is x^3 - 3x^2 + 9x - 27 and there is no remainder since the last number is 0. Therefore, the result of dividing x^4 + 81 by x + 3 is x^3 - 3x^2 + 9x - 27.

Answer 2

x^3 + 3x^2 + 9x + 27

Step-by-step explanation:

Hope this helps!