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Chapter 2: Problem 42

Use synthetic division to divide. $$\frac{-3 x^{4}}{x+2}$$

Short Answer

Expert verified
After conducting synthetic division, the result is \(\ -3x^{3} + 6x^{2} - 12x + 24 \).

Step by step solution

01

Setup Synthetic Division Grid

First off, set up the synthetic division grid by writing the coefficients of \( -3x^{4} \) and the constant term on top. In this case, the coefficients are \( -3 \), \( 0 \), \( 0 \), \( 0 \) and \( 0 \) (the zeros are for missing powers of x). The divisor \( x+2 \) gives us the number -2 which should be placed on the left outside the grid.
02

Conduct Synthetic Division

Next, start escalating the bottom row in accordance to synthetic division rules: \n1. The first coefficient, -3, is dropped down in the first column, producing the start of the quotient polynomial. \n2. Multiply -2 (on the left most outside the grid) by -3 (under the grid). Write the result underneath the next coefficient (0), in the second column. \n3. Finally, add the numbers in the second column to obtain a result. Repeat the multiply and add process.
03

Interpret the result

Now, interpret the result of synthetic division. We must remember to decrement the degree of each term in the quotient by 1. The bottom row of the synthetic division grid decodes into: \(\ -3x^{3} + 6x^{2} - 12x + 24 \). This is the answer quotient polynomial with degree reduced by 1 at each variable term.

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