(d) x4 - 6x3 + 6x2 + 12x + 6 by x2 - 6
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Answers
Step-by-step explanation:
x
3
−
6
x
2
+
12
x
−
8
x
−
2
=
x
2
−
4
x
+
4
Explanation:
One way to solve this problem is to perform polynomial long division. We write the polynomial and its divisor down in long division form and work through the normal steps of long division. Then we guess our first term in the quotient, which should subtract from the first term in the dividend shown in
red
below:
x
2
−
4
x
+
4
x
−
2
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
)
x
3
−
6
x
2
+
12
x
−
8
−
x
3
+
2
x
2
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
−
4
x
2
+
12
x
4
x
2
−
8
x
¯¯¯¯¯¯¯¯¯¯¯¯¯¯
4
x
−
8
−
4
x
+
8
¯¯¯¯¯¯¯¯¯¯¯¯
0
We then repeat this step for the next powers of
x
shown in
blue
and
green
. We end up with a zero remainder.
x
3
−
6
x
2
+
12
x
−
8
x
−
2
=
x
2
−
4
x
+
4
Answer:
X3
Step-by-step explanation: