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Byju's Answer
Standard VIII
Mathematics
Multiplication of Any Polynomial
Coefficient o...
Question
Coefficient of x
19
in the polynomial
(
x
−
1
)
(
x
−
2
)
.
.
.
.
.
.
.
.
.
.
(
x
−
20
)
is equal to
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Solution
The Given equation is
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
.
.
.
.
(
x
−
19
)
(
x
−
20
)
Consider the first 2 factors
(
x
−
1
)
and
(
x
−
2
)
(
x
−
1
)
(
x
−
2
)
=
x
2
−
(
1
+
2
)
x
1
+
(
1
×
2
)
Similarly, for the rest of the terms, we can write ,
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
.
.
.
.
(
x
−
19
)
(
x
−
20
)
=
x
20
−
(
1
+
2
+
3
+
.
.
.
.
.
.
.
+
19
+
20
)
x
19
+
(
1
×
2
+
2
×
3
+
.
.
.
.
.
.
19
×
20
)
x
18
∴
Coefficient of
x
19
=
−
(
1
+
2
+
3
+
.
.
.
.
.
.
.
.
.
.
+
19
+
20
)
=
−
[
20
2
(
1
+
20
)
]
=
−
10
×
21
=
−
210
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