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(20055)   (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).

Start with this:

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
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
There are two ways to do this:


Direct Substitution and Evaluation Method:

Start with the given equation.


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|3-832-1614
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 3)
3|3-832-1614
|
3

Multiply 3 by 3 and place the product (which is 9) right underneath the second coefficient (which is -8)
3|3-832-1614
|9
3

Add 9 and -8 to get 1. Place the sum right underneath 9.
3|3-832-1614
|9
31

Multiply 3 by 1 and place the product (which is 3) right underneath the third coefficient (which is 3)
3|3-832-1614
|93
31

Add 3 and 3 to get 6. Place the sum right underneath 3.
3|3-832-1614
|93
316

Multiply 3 by 6 and place the product (which is 18) right underneath the fourth coefficient (which is 2)
3|3-832-1614
|9318
316

Add 18 and 2 to get 20. Place the sum right underneath 18.
3|3-832-1614
|9318
31620

Multiply 3 by 20 and place the product (which is 60) right underneath the fifth coefficient (which is -16)
3|3-832-1614
|931860
31620

Add 60 and -16 to get 44. Place the sum right underneath 60.
3|3-832-1614
|931860
3162044

Multiply 3 by 44 and place the product (which is 132) right underneath the sixth coefficient (which is 14)
3|3-832-1614
|931860132
3162044

Add 132 and 14 to get 146. Place the sum right underneath 132.
3|3-832-1614
|931860132
3162044146


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


So according to the remainder theorem, this means that
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