Problem 43 Use synthetic division to divide... [FREE SOLUTION]

Chapter 2: Problem 43

Use synthetic division to divide. \(\frac{180 x-x^{4}}{x-6}\)

Short Answer

Expert verified

The result of the division of \(-x^{4} + 180x\) by \(x - 6\) is \(-x^{3} - 6x^{2} - 36x - 216\).

Step by step solution

Identify coefficients

Identify the coefficients of the dividend (the polynomial being divided). In this case, it's \(-x^{4} + 180x\). This equates to \(-1, 0, 0, 180, 0\). The coefficients are \(-1, 0, 0, 180, 0\) because there are no terms for \(x^{3}\), \(x^{2}\) and the constant term in the dividend.

Set up the synthetic division tableau

The synthetic division tableau is set up as follows: Write the coefficients of the dividend on the top of the tableau. The divisor is \(x - 6\), so you would write '+6' to the left of the vertical line. As mentioned, remember to include zeroes for any missing degree terms of the dividend.

Perform synthetic division

Bring down the first coefficient (which is -1). Multiply 6 (from 'x - 6') by -1 and write the result under the second coefficient. Add vertically. Repeat this process until all coefficients in the dividend have been processed. The result will be the coefficients of the quotient.

Interpret the result

The result of the synthetic division are the coefficients of the polynomial quotient from the division. The degree of the quotient polynomial is one less than the degree of the original dividend, and it has the coefficients derived from the synthetic division.

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91影视

Use synthetic division to divide. \(\frac{180 x-x^{4}}{x-6}\)

Short Answer

Step by step solution

Identify coefficients

Set up the synthetic division tableau

Perform synthetic division

Interpret the result

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