Divide 3x5 + 2x2 + x - x4 + 2 by 3x2 – 2x - 3 using both Long Division and Synthetic Division. Compare your quotients in both methods.
Answers
Answer:
2
x
2
+
3
x
+
4
Explanation:
The first thing we must do is find the value that makes
x
−
3
equal to zero. In this case,
x
=
3
. This will be our divisor.
Now, we set up the problem:
If we have
2
x
3
−
3
x
2
−
5
x
−
12
3
.
∣
2
3
.
−
3
3
.
−
5
3
.
−
12
3
.
∣
______
Now, we bring down the
2
and multiply it by the
3
, like this:
3
.
∣
2
3
.
−
3
3
.
−
5
3
.
−
12
3
.
∣
__
6
____
...
...
.
2
Now we add the
−
3
to the
6
, which gives us
3
. I'll show you what I mean.
3
.
∣
2
3
.
−
3
3
.
−
5
3
.
−
12
3
.
∣
__
6
___9_12__.2.3.4.0
I just did the whole thing, and I hope you can see what I did. I took the sum of the answer and multiplied it to the divisor, 3. Then I take the product and place it in the next column. Then, I add the column together, and whatever the answer is, I multiply it to the 3.
Anyways, we take the leftover number as the bottom, the 2.3.4.0
and rewrite them as an equation, like this: 2x2+3x+4
. We can factor this further if we want, but I'm going to stop there.
Answer:
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