Part 3 of 5
Now, given that g(x) = -82³-92-8090, use synthetic division and the Remainder Theorem to find
g(-10).
g(-10) =
Add Work
To find g(-10), we will use synthetic division and the Remainder Theorem.
First, let's set up the synthetic division:
-10 | -82 0 -92 -8090
_________________
We start by bringing down the first coefficient, which is -82.
-10 | -82 0 -92 -8090
_________________
-82
Next, we multiply -10 by -82 and write the result in the next column:
-10 | -82 0 -92 -8090
_________________
-82
+820
We then add the values in the second column:
-10 | -82 0 -92 -8090
_________________
-82
+820
_______
738
Next, we multiply -10 by 738 and write the result in the next column:
-10 | -82 0 -92 -8090
_________________
-82
+820
_______
738
-7380
We then add the values in the third column:
-10 | -82 0 -92 -8090
_________________
-82
+820
_______
738
-7380
_______
-6642
Finally, we multiply -10 by -6642 and write the result in the next column:
-10 | -82 0 -92 -8090
_________________
-82
+820
_______
738
-7380
_______
-6642
+66420
We then add the values in the fourth column:
-10 | -82 0 -92 -8090
_________________
-82
+820
_______
738
-7380
_______
-6642
+66420
________
59778
The remainder is 59778.
According to the Remainder Theorem, the remainder when g(x) is divided by x + 10 is equal to g(-10).
Therefore, g(-10) = 59778.