To divide 4x3 - 8x - 2 by x + 5 using synthetic division, the first step is to write   __l__ __ __ __

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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To divide 4x3 - 8x - 2 by x + 5 using synthetic division, the first step is to write   __l__ __ __ __

Expert Solution
Step 1: Here we have to use synthetic division.

 The synthetic division is another way to divide a polynomial by the binomial x-c, where c is a constant.

Given polynomial is  f(x)=4x3-8x-2 and we have to divide it by x+5.

Step 1) Set up the synthetic division.

    First write given polynomial in decreasing order.

   So we get, 

      f(x) = 4x3+0x2-8x-2

 And now set up the division,

                               coefficient of dividend   -5          40-8-2

 

Step 2

Step 2) Bring down the leading coefficient to the bottom row.

                -5          40-8-2                      4

Step 3)  Multiply c=-5 by the value just written on bottom row and place this value right beneath

          the next coefficient in the dividend.

        

Step 4) Add the column created in step 3. and write the sum in the bottom row.

Step  5) Repeat until done.

Step 6) Write the answer.

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