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Let , where is a non-zero…
MATHEMATICS · Multi-part · GCSE · Mathematics · Algebra · Algebra
Problem
Let
g
(
x
)
=
x
3
+
k
x
2
−
4
k
x
−
4
k
g(x)=x^{3}+kx^{2}-4kx-4k
g
(
x
)
=
x
3
+
k
x
2
−
4
k
x
−
4
k
, where
k
k
k
is a non-zero integer. (i) Given that
x
=
2
x=2
x
=
2
is a zero of
g
(
x
)
g(x)
g
(
x
)
, find the value of
k
k
k
. (ii) For the value of
k
k
k
obtained in part (i), factorise
g
(
x
)
g(x)
g
(
x
)
completely. (iii) Write all the zeros of
g
(
x
)
g(x)
g
(
x
)
for this value of
k
k
k
.
Related theory
Factorisation of Polynomials
Polynomials
Polynomial Functions
Algebra
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