A(1,2),B(2,-3) and c(-2,3) are three points A point p moves such that PA2+PB2 =2pc2 .show that the equation to the locus of p is 7x-7y+4=c
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Answer:
First notice that substituting
x
=
1
results in
x
3
−
3
x
+
2
=
0
So
(
x
−
1
)
is a factor.
Use synthetic division to find the remaining factor...
x
3
−
3
x
+
2
=
(
x
−
1
)
(
x
2
+
x
−
2
)
Notice that
x
=
1
is also a root of
x
2
+
x
−
2
So we have another
(
x
−
1
)
factor...
x
2
+
x
−
2
=
(
x
−
1
)
(
x
+
2
)
So the complete factorization is:
x
3
−
3
x
+
2
=
(
x
−
1
)
(
x
−
1
)
(
x
+
2
)
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