SOLUTION: Use synthetic substitution to find: f(-4) for f(x)=x³+3x -5x-7

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Question 181392: Use synthetic substitution to find:
f(-4) for f(x)=x³+3x -5x-7
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I presume you meant:



Write the substitution value on the left, draw a vertical line, then write the coefficients of the polynomial. Leave a space below and then draw a horizontal. Then drop the first coefficient below the line.






Multiply the substitution value by the number below the line and put it below the second coefficient:







Add the column just created:







Repeat the process:







Repeat the process again:








The last addition result is the value of the function when the given value is substituted for the independent variable, hence

John

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Use synthetic substitution to find:
f%28-4%29 for f%28x%29=x%5E3%2B3x%5E2-5x-7

There are two ways to substitute a number for x 
in a polynomial:

1. Direct substitution  (a harder method)

f%28x%29=x%5E3%2B3x%5E2-5x-7

Replace x by -4

f%28-4%29=%28-4%29%5E3%2B3%28-4%29%5E2-5%28-4%29-7

f%28-4%29=%28-4%29%28-4%29%28-4%29%2B3%28-4%29%28-4%29-5%28-4%29-7

f%28-4%29=-64%2B48%2B20-7

f%28-4%29=-3

So the answer is -3.  However that's by
direct substitution.  That's not what you
are supposed to do.  You are to use 
synthetic substitution, which is easier.

2. Synthetic substitution. (easier)

f%28x%29=x%5E3%2B3x%5E2-5x-7.  Put the -4
on the left of a synthetic division array:

-4|1   3   -5   -7
  |   -4    4    4
   1  -1   -1   -3

The answer is the number on the bottom
right, the -3, so

f(-4) = -3 

Notice that you get -3 either by direct
substitution and by synthetic substitution.

Edwin