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Let and . Define…
MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials
Problem
Let
f
(
x
)
=
x
4
−
6
x
2
+
8
f(x)=x^{4}-6x^{2}+8
f
(
x
)
=
x
4
−
6
x
2
+
8
and
g
(
x
)
=
−
2
x
5
+
x
3
g(x)=-2x^{5}+x^{3}
g
(
x
)
=
−
2
x
5
+
x
3
. Define
h
(
x
)
=
f
(
x
)
g
(
x
)
h(x)=f(x)\,g(x)
h
(
x
)
=
f
(
x
)
g
(
x
)
. (i) Find the degree of
h
(
x
)
h(x)
h
(
x
)
. (ii) Find the leading coefficient of
h
(
x
)
h(x)
h
(
x
)
. (iii) State whether
h
(
x
)
h(x)
h
(
x
)
is an even function, an odd function or neither, giving a brief reason.
Related theory
Polynomial Functions
Polynomials
Functions
Quadratic graphs and extrema
Algebra
Polynomials in one variable
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