solve problem

Question

Use synthetic division to find the function value.

 

f(x)=2x⁵-2x³-17x²-1648,  find f(4)

Answer 1

f(x)=2x⁵-2x³-17x²-1648,  find f(4)

 

First we need to fill in the polynomial to include any missing exponents

because we need all exponents of x from 5 to 0

 

2x⁵ + 0x⁴ -2x³ -17x² + 0x -1648

 

Write out all the coefficients in a line with the number to evaluated to the left

 

4   /   2     0     -2     -17         0     -1648

    /          8    32     120       412      1648

    _______________________________

   

        2       8    30      103    412        0

 

What we did was:

1) bring down the first coefficient

2) multiply that number by 4 and bring the result up under the 2nd coefficient

    This brought 8 up under the 0...  Add those 2 numbers and bring down

3) Multiply this new number by 4 and bring up under the 3rd coefficient and add down again

    This gave 4(8) = 32 which we placed under the -2 and added to get 30

Continue this process to the end.

 

The last sum (the number on the bottom right) is the answer to f(4)

 

f(4) = 0

 

Answer 2

OK, Billy, I hope I can still help!

 

First, we have to write out our coefficients. They are 2,0,-2,-17,0,-1648

 

Now, we plug in our 4 to look something like this...

 

4         2   0    -2    -17    0    -1648

 

We are going to bring down the first number, multiply it by 4, put it under the next number, add the two, repeat...

 

4          2         0      -2     -17       0      -1648

                      8       32    120     512     2048

            2        8       30     103    512       400

 

The last number on the at the end is our answer.  f(4) = 400

 

Hope this helps!