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Use synthetic division to find P(–3)
(
–
3
)
for P(x)=x4–2x3–4x+4
(
)
=
4
–
2
3
–
4
+
4
.
To use synthetic division, we set up the equation using the given polynomial and the value of -3.
The equation is: (x^4 - 2x^3 - 4x + 4) ÷ (-3)
Using synthetic division, we set up the division table as follows:
-3 | 1 -2 -4 0 4
----------------------
We start by bringing down the first coefficient, which is 1.
-3 | 1 -2 -4 0 4
----------------------
1
Next, we multiply the divisor (-3) by the number on the bottom and write the result below the next coefficient.
-3 | 1 -2 -4 0 4
----------------------
1
-3
We then add the two numbers in the row, below the line, to get the result.
-3 | 1 -2 -4 0 4
----------------------
1
-3
------
-1
Next, we repeat the process by multiplying the divisor (-3) by the result (-1) and write the result below the next coefficient.
-3 | 1 -2 -4 0 4
----------------------
1 2
-3
------
-1
3
We add the two numbers in the row, below the line, to get the result.
-3 | 1 -2 -4 0 4
----------------------
1 2
-3
------
-1
3
------
2
We repeat this process until all the coefficients have been brought down and the division is complete.
-3 | 1 -2 -4 0 4
----------------------
1 2 2 6 18
-3
------
-1
3
------
2
-6
------
-2
The remainder is the number at the bottom of the division table, which in this case is -2.
Therefore, P(-3) is -2.