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Mathematics
Mathematics
Problem
a. (i) Divide
4
x
4
+
7
x
3
−
2
x
2
+
x
−
9
4x^{4}+7x^{3}-2x^{2}+x-9
4
x
4
+
7
x
3
−
2
x
2
+
x
−
9
by
x
2
+
x
+
1
x^{2}+x+1
x
2
+
x
+
1
and write the quotient
q
(
x
)
q(x)
q
(
x
)
and the remainder
r
(
x
)
r(x)
r
(
x
)
. b. (ii) Using your result from part (i), verify that
4
x
4
+
7
x
3
−
2
x
2
+
x
−
9
=
(
x
2
+
x
+
1
)
q
(
x
)
+
r
(
x
)
.
4x^{4}+7x^{3}-2x^{2}+x-9=(x^{2}+x+1)q(x)+r(x).
4
x
4
+
7
x
3
−
2
x
2
+
x
−
9
=
(
x
2
+
x
+
1
)
q
(
x
)
+
r
(
x
)
.
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