# SOLUTION: If P(x) = 3x^5 - 8x^4 + 3x^3 + 2x^2 - 16x + 14, then P(3) = ? ...is it 682?

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Question 194080This question is from textbook Saxon Algebra 2
: If P(x) = 3x^5 - 8x^4 + 3x^3 + 2x^2 - 16x + 14, then P(3) = ?
...is it 682?
This question is from textbook Saxon Algebra 2

Found 2 solutions by Edwin McCravy, jim_thompson5910:
Answer by Edwin McCravy(8908)   (Show Source):
You can put this solution on YOUR website!
If P(x) = 3x^5 - 8x^4 + 3x^3 + 2x^2 - 16x + 14, then P(3) = ?
...is it 682?
```
No it isn't.

There are two ways to find P(3).

Method 1.  Substitute 3 for x in

Method 2 (Much easier, by synthetic division).

3 | 3 -8  3   2 -16   14
|
---------------------

and end up with this:

3 | 3 -8  3   2 -16   14
|    9  3  18  60  132
---------------------
3  1  6  20  44  146

The answer, 146, is in the lower right
corner of the synthetic division.

Edwin```

You can put this solution on YOUR website!
There are two ways to do this:

Direct Substitution and Evaluation Method:

Plug in .

Raise to the 5th power to get .

Raise to the 4th power to get .

Cube to get .

Square to get .

Multiply and to get .

Multiply and to get .

Multiply and to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

--------------------------------------------------------------------------------

OR....

Synthetic Division Method:

First lets find our test zero:

Set the denominator equal to zero

Solve for x.

so our test zero is 3

Now set up a synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the function to the right of the test zero.
 3 | 3 -8 3 2 -16 14 |

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 3)
 3 | 3 -8 3 2 -16 14 | 3

Multiply 3 by 3 and place the product (which is 9) right underneath the second coefficient (which is -8)
 3 | 3 -8 3 2 -16 14 | 9 3

Add 9 and -8 to get 1. Place the sum right underneath 9.
 3 | 3 -8 3 2 -16 14 | 9 3 1

Multiply 3 by 1 and place the product (which is 3) right underneath the third coefficient (which is 3)
 3 | 3 -8 3 2 -16 14 | 9 3 3 1

Add 3 and 3 to get 6. Place the sum right underneath 3.
 3 | 3 -8 3 2 -16 14 | 9 3 3 1 6

Multiply 3 by 6 and place the product (which is 18) right underneath the fourth coefficient (which is 2)
 3 | 3 -8 3 2 -16 14 | 9 3 18 3 1 6

Add 18 and 2 to get 20. Place the sum right underneath 18.
 3 | 3 -8 3 2 -16 14 | 9 3 18 3 1 6 20

Multiply 3 by 20 and place the product (which is 60) right underneath the fifth coefficient (which is -16)
 3 | 3 -8 3 2 -16 14 | 9 3 18 60 3 1 6 20

Add 60 and -16 to get 44. Place the sum right underneath 60.
 3 | 3 -8 3 2 -16 14 | 9 3 18 60 3 1 6 20 44

Multiply 3 by 44 and place the product (which is 132) right underneath the sixth coefficient (which is 14)
 3 | 3 -8 3 2 -16 14 | 9 3 18 60 132 3 1 6 20 44

Add 132 and 14 to get 146. Place the sum right underneath 132.
 3 | 3 -8 3 2 -16 14 | 9 3 18 60 132 3 1 6 20 44 146

Since the last column adds to 146, we have a remainder of 146.

So according to the remainder theorem, this means that