SOLUTION: This test is very difficult and any help would be so very much appriciated, please reply asap. The problem is: Use synthetic substitution to find F(4) given {{{F(x)=2x^3-5x^2-18

Algebra ->  Test -> SOLUTION: This test is very difficult and any help would be so very much appriciated, please reply asap. The problem is: Use synthetic substitution to find F(4) given {{{F(x)=2x^3-5x^2-18      Log On


   



Question 122887: This test is very difficult and any help would be so very much appriciated, please reply asap. The problem is:
Use synthetic substitution to find F(4) given F%28x%29=2x%5E3-5x%5E2-18x%2B19

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find f%284%29, we can use synthetic division.


Set up the synthetic division table by placing the value we want to evaluate (in this case 4) in the upper left corner and placing the coefficients of the polynomial to the right of the test zero.
4|2-5-1819
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2)
4|2-5-1819
|
2

Multiply 4 by 2 and place the product (which is 8) right underneath the second coefficient (which is -5)
4|2-5-1819
|8
2

Add 8 and -5 to get 3. Place the sum right underneath 8.
4|2-5-1819
|8
23

Multiply 4 by 3 and place the product (which is 12) right underneath the third coefficient (which is -18)
4|2-5-1819
|812
23

Add 12 and -18 to get -6. Place the sum right underneath 12.
4|2-5-1819
|812
23-6

Multiply 4 by -6 and place the product (which is -24) right underneath the fourth coefficient (which is 19)
4|2-5-1819
|812-24
23-6

Add -24 and 19 to get -5. Place the sum right underneath -24.
4|2-5-1819
|812-24
23-6-5

Since the last column adds to -5, we have a remainder of -5. This means x-4 is not a factor of 2x%5E3+-+5x%5E2+-+18x+%2B+19

Since the remainder is -5, this means f%284%29=-5


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Answer:

So f%284%29=-5