factorise x^4 + 3x^3 + 3x^2 + x + 1
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Answer:
x
4
+
2
x
3
+
3
x
2
+
2
x
+
1
=
(
x
2
+
a
x
+
1
)
(
x
2
+
b
x
+
1
)
Multiply the factors on the right:
x
4
+
2
x
3
+
3
x
2
+
2
x
+
1
=
x
4
+
(
a
+
b
)
x
3
+
(
a
b
+
2
)
x
2
+
(
a
+
b
)
x
+
1
So
a
+
b
=
2
, thus
b
=
2
−
a
a
b
=
a
(
2
−
1
)
=
1
, thus
a
2
−
2
a
+
1
=
0
The only root for
a
is
a
=
1
, then also
b
=
1
and we end up with:
x
4
+
2
x
3
+
3
x
2
+
2
x
+
1
=
(
x
2
+
x
+
1
)
2
.
Step-by-step explanation:
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