How do I use synthetic division to find the quotient and the remainder of a problem that has exponents in the equation?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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How do I use synthetic division to find the quotient and the remainder of a problem that has exponents in the equation?

 

Expert Solution
Step 1

Let us have to divide (2x3-4x2+x-5) by (x-2) using synthetic division. 

Then we will consider the coefficients of (2x3-4x2+x-5) , which are 2 , - 4 , 1 , -5 

For x-2 , we set it equal to 0 , so we get x-2=0 or x=2

We will divide by this x=2

The first-term goes down as it is, then we multiply it by the 2, and the result goes below -4. Then add them.

Then again multiply the result by 2 and that goes below 1. Then again add and multiply. This process continues. 

Algebra homework question answer, step 1, image 1

So the coefficients of the quotient are: 2 , 0 , 1

So the quotient is: 2x2+0x+1=2x2+1 

Remainder = -3

 

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