SOLUTION: Can someone please help me with this problem? The last line of synthetic division for (2x^4-5x^3+7x^2-3x+1)/(x-3) gives coefficients for the quotient of 2,1,8,21. Is this true or

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Question 124378: Can someone please help me with this problem?
The last line of synthetic division for (2x^4-5x^3+7x^2-3x+1)/(x-3) gives coefficients for the quotient of 2,1,8,21.
Is this true or false?
I thought the answer was false. Am I right please help!!!
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let's simplify this expression using synthetic division

Start with the given expression

First lets find our test zero:

Set the denominator equal to zero

Solve for x.

so our test zero is 3

Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.

3 | 2 -5 7 -3 1
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2)

3 | 2 -5 7 -3 1
|
2

Multiply 3 by 2 and place the product (which is 6) right underneath the second coefficient (which is -5)

3 | 2 -5 7 -3 1
| 6
2

Add 6 and -5 to get 1. Place the sum right underneath 6.

3 | 2 -5 7 -3 1
| 6
2 1

Multiply 3 by 1 and place the product (which is 3) right underneath the third coefficient (which is 7)

3 | 2 -5 7 -3 1
| 6 3
2 1

Add 3 and 7 to get 10. Place the sum right underneath 3.

3 | 2 -5 7 -3 1
| 6 3
2 1 10

Multiply 3 by 10 and place the product (which is 30) right underneath the fourth coefficient (which is -3)

3 | 2 -5 7 -3 1
| 6 3 30
2 1 10

Add 30 and -3 to get 27. Place the sum right underneath 30.

3 | 2 -5 7 -3 1
| 6 3 30
2 1 10 27

Multiply 3 by 27 and place the product (which is 81) right underneath the fifth coefficient (which is 1)

3 | 2 -5 7 -3 1
| 6 3 30 81
2 1 10 27

Add 81 and 1 to get 82. Place the sum right underneath 81.

3 | 2 -5 7 -3 1
| 6 3 30 81
2 1 10 27 82

Since the last column adds to 82, we have a remainder of 82. This means is not a factor of
Now lets look at the bottom row of coefficients:

Looking at the last line, we see the coefficients: 2,1,10, and 27

So the coefficients for the quotient are not 2,1,8, and 21

So the answer is false and you are correct.

Answer by Edwin McCravy(20086) (Show Source):
You can put this solution on YOUR website!
Can someone please help me with this problem?
The last line of synthetic division for (2x^4-5x^3+7x^2-3x+1)/(x-3) gives coefficients for the quotient of 2,1,8,21.
Is this true or false?
I thought the answer was false. Am I right please help!!!

We'll have to do it and see. There's no other way: 3|2 -5 7 -3 1 | 6 3 30 81 2 1 10 27 82 What that tells us is that the coefficients for the quotient are 2, 1, 10, and 27 and that the remainder is 82. That means that the quotient is or, erasing the 1 coefficient on : So the answer is indeed false, but getting it right simply by lucky guessing would most likely not be acceptable to your teacher. Edwin