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Chapter 5: Q.320. (page 551)

Use synthetic division to find the quotient and remainder.

x4+13x2+13x+3is divided byx+3

Short Answer

Expert verified

The quotient is x3-3x2+22x+53and the remainder is -156.

Step by step solution

01

Step 1. Given information.

x4+13x2+13x+3is divided byx+3

02

Step 2. Write the dividend with decreasing power of x.

x4+0x3+13x2+13x+13

03

Step 3. Write the coefficients of the terms as the first row of the synthetic division. 

Write the divisor form of x-cthat is x--3.

-31013133

04

Step 4. Bring down the first coefficient to the third row and multiply the coefficients by the divisor and place the result in the second row and add the column and put the result in the third row. 

-31013133-39-66-1591-32253-156炉

05

Step 4. Simplified answer. 

The coefficients of the quotient are 1,-3,22,53.

The quotient isrole="math" localid="1644402541115" x3-3x2+22x+53and the remainder is-156.

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