How do you factor 6x^4y^3 + 21x^3y^2 − 9x^2y?
Answers
Answered by
3
Explaination
First notice that all of the terms are divisible by
3
x
2
y
, so separate that out as a factor:
6
x
4
y
3
+
21
x
3
y
2
−
9
x
2
y
=
3
x
2
y
(
2
x
2
y
2
+
7
x
y
−
3
)
The remaining factor is a quadratic in
x
y
, whose zeros we can find using the quadratic formula:
x
y
=
−
7
±
√
7
2
−
(
4
⋅
2
⋅
−
3
)
2
⋅
2
=
−
7
±
√
49
+
24
4
=
−
7
±
√
73
4
Hence:
2
x
2
y
2
+
7
x
y
−
3
=
2
(
x
y
+
7
4
−
√
73
4
)
(
x
y
+
7
4
+
√
73
4
)
Putting it all together:
6
x
4
y
3
+
21
x
3
y
2
−
9
x
2
y
=
3
x
2
y
(
2
x
2
y
2
+
7
x
y
−
3
)
=
6
x
2
y
(
x
y
+
7
4
−
√
73
4
)
(
x
y
+
7
4
+
√
73
4
)
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