SOLUTION: Use synthetic division to determine f(-3) if f(x)=4x^3-3x^2-5x+9 any help would be appreciated!! here are the choices: A.-111 B.75 C.9 D.-36 thanks again

Question 189558: Use synthetic division to determine f(-3) if f(x)=4x^3-3x^2-5x+9
any help would be appreciated!!
here are the choices:
A.-111
B.75
C.9
D.-36
thanks again
Found 2 solutions by Kalmetam, jim_thompson5910:
Answer by Kalmetam(43) (Show Source): You can put this solution on YOUR website!
Use synthetic division to determine f(-3) if f(x)=4x^3-3x^2-5x+9

Ok all you need to do is plug in the -3 in as x
So it would start off as (with leaving off the f(x):

NO Multiplying with the parentheses
Now we just solve the problems IN the parentheses:

Continue...

Take everything out:

Then solve
-111 should be the answer
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The last post is correct (even though weird notation was used), but s/he didn't use synthetic division.

Note: the test zero is x=-3

First 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 | 4 -3 -5 9
|

Now bring down the leading coefficient (it is the coefficient with the highest exponent which is 4)

-3 | 4 -3 -5 9
|
4

Multiply -3 by 4 and place the product (which is -12) right underneath the second coefficient (which is -3)

-3 | 4 -3 -5 9
| -12
4

Add -12 and -3 to get -15. Place the sum right underneath -12.

-3 | 4 -3 -5 9
| -12
4 -15

Multiply -3 by -15 and place the product (which is 45) right underneath the third coefficient (which is -5)

-3 | 4 -3 -5 9
| -12 45
4 -15

Add 45 and -5 to get 40. Place the sum right underneath 45.

-3 | 4 -3 -5 9
| -12 45
4 -15 40

Multiply -3 by 40 and place the product (which is -120) right underneath the fourth coefficient (which is 9)

-3 | 4 -3 -5 9
| -12 45 -120
4 -15 40

Add -120 and 9 to get -111. Place the sum right underneath -120.

-3 | 4 -3 -5 9
| -12 45 -120
4 -15 40 -111

Since the last column adds to -111, we have a remainder of -111.

So according to the remainder theorem, this means that which tells us that the answer is A.
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