Use synthetic division to find P(-3) for
P(x) = -2x^4 + 6x^2 - x + 1
please show your work! ^.^
the instructions were to use synthetic division, idk why... thank you very much! i appreciate it :)
Google "synthetic division" you'll get many websites.
It is hard to show the algorithm with the format of Jiskha
btw, why use synthetic division to find P(-3) ?? , just evaluate
P(-3) = -2(-3)^4 + 6(-3)^2 - (-3) + 1
= -162 + 54 + 3 + 1
= -104
To find P(-3), we can use synthetic division. Here are the steps:
1. Set up the synthetic division table:
-3 | -2 0 6 -1 1
2. Bring down the coefficient of the highest power term, which is -2:
-3 | -2 0 6 -1 1
-2
3. Multiply the number at the top by -3 and write the result under the next coefficient:
-3 | -2 0 6 -1 1
-2
--------
6
4. Add the result to the next coefficient:
-3 | -2 0 6 -1 1
-2
--------
6 0
5. Repeat steps 3 and 4 until you reach the constant term:
-3 | -2 0 6 -1 1
-2 -12
--------
6 0 -6
--------
-1
6. The number at the bottom is the remainder. The other numbers are the coefficients of the quotient. In this case, the quotient is -2x^3 - 12x + 6. The remainder is -1.
Therefore, P(-3) = -1.
To use synthetic division to find P(-3) for the polynomial P(x) = -2x^4 + 6x^2 - x + 1, follow these steps:
Step 1: Write down the coefficients of the polynomial in descending order of powers of x. In this case, the coefficients are:
-2, 0, 6, -1, 1
Step 2: Set up the synthetic division table by writing down the value we are substituting, which is -3, on the left side, and then write down the coefficients of the polynomial.
-3 | -2 0 6 -1 1
Step 3: Bring down the first coefficient, which is -2, underneath the division line.
-3 | -2 0 6 -1 1
---------------------------
| | |
|________________|
Step 4: Multiply the divisor, -3, by the first number, -2, and write the result under the second coefficient.
-3 | -2 0 6 -1 1
---------------------------
6
Step 5: Add the result to the next coefficient, which is 0. Write the sum underneath the line.
-3 | -2 0 6 -1 1
---------------------------
6
+ 0
Step 6: Repeat steps 4 and 5 until all coefficients have been processed.
-3 | -2 0 6 -1 1
---------------------------
6
+ 0
0
0
3
Step 7: Read the numbers at the bottom of the table. The last number, 3, is the remainder.
Step 8: The expression P(-3) is equal to the remainder, which is 3.
Therefore, P(-3) = 3.