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Byju's Answer
Standard IX
Mathematics
Factorisation of a Polynomial
check whether...
Question
check whether g(x) is a factor of p(x)
p(x)= 8x
3
-6x
2
-4x+3
g(x)= x/3-1/4
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Solution
p(x)= 8x
3
-6x
2
-4x+3
g(x)= x/3-1/4
that is, x=3/4
put value of x in p(x)
p(3/4)=8*(27/64)-6*(9/16)-4*(3/4)+3
=(27/8)-(27/8)-3+3
=0
therefore g(x) is a factor of p(x)
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By Remainder theorem, find the remainder when p(x) is divided by g(x).
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p
(
x
)
=
x
3
–
2
x
2
–
4
x
–
1
,
g
(
x
)
=
x
+
1
(ii)
p
(
x
)
=
x
3
–
3
x
2
+
4
x
+
50
,
g
(
x
)
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3
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p
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x
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=
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x
3
–
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g
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x
–
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(iv)
p
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x
)
=
x
3
–
6
x
2
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2
x
−
4
,
g
(
x
)
=
1
−
3
2
x
Q.
Question 15
Check whether p(x) is a multiple of g(x) or not:
(i)
p
(
x
)
=
x
3
–
5
x
2
+
4
x
–
3
,
g
(
x
)
=
x
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3
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x
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x
)
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