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Let , where is a real number. (i) Find the value of for which is a factor of . (ii)…
MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials
Problem
Let
p
(
x
)
=
k
x
3
+
(
k
+
1
)
x
2
−
(
2
k
−
3
)
x
−
6
p(x)=kx^{3}+(k+1)x^{2}-(2k-3)x-6
p
(
x
)
=
k
x
3
+
(
k
+
1
)
x
2
−
(
2
k
−
3
)
x
−
6
, where
k
k
k
is a real number. (i) Find the value of
k
k
k
for which
(
x
−
2
)
(x-2)
(
x
−
2
)
is a factor of
p
(
x
)
p(x)
p
(
x
)
. (ii) Using the value of
k
k
k
obtained in part (i), factorise
p
(
x
)
p(x)
p
(
x
)
completely.
Related theory
Factorisation of Polynomials
Polynomials
Polynomial Functions
Functions
Algebra
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