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Mendations Skill plans als using synthetic division D^(6)D (x^(3)+21x^(2)+15)-:(x+1)

User Larsks
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Final answer:

The question involves using synthetic division to divide the polynomial x^3 + 21x^2 + 15 by x + 1. The outcome of the process is a quadratic polynomial x^2 + 20x - 20 with a remainder of -5.

Step-by-step explanation:

The question is asking to divide a polynomial, x3 + 21x2 + 15, by another polynomial, x + 1, using synthetic division. Synthetic division is a simplified form of polynomial division, used when dividing by a linear factor, and particularly useful when the divisor is in the form x - c.

To use synthetic division, we first identify the value that x needs to be for the divisor to equal zero, which is -1 in this case since x + 1 = 0 when x = -1. Next, we list the coefficients of the dividend: 1 (for x3), 21 (for x2), 0 (since there is no x term, we use a placeholder), and 15 (the constant term).

We then bring down the leading coefficient (1) and proceed with the synthetic division process:

  1. Multiply the value brought down by -1 and write the result under the next coefficient (21).
  2. Add this result to the next coefficient and write the sum underneath.
  3. Repeat the above two steps for the remaining coefficients.

Carrying out the steps, the synthetic division would look something like this:

-1 | 1 21 0 15
|___________________
| 1 20 -20 -5

The result of the division is x2 + 20x - 20 with a remainder of -5.

User Frishi
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