Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Let f(x)=(x+2)^2(x-2)^2-(x^4-16)
MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials
Problem
Let
f
(
x
)
=
(
x
+
2
)
2
(
x
−
2
)
2
−
(
x
4
−
16
)
.
f(x)=(x+2)^2(x-2)^2-(x^4-16).
f
(
x
)
=
(
x
+
2
)
2
(
x
−
2
)
2
−
(
x
4
−
16
)
.
(i) Simplify
f
(
x
)
f(x)
f
(
x
)
and express it as a polynomial in descending powers of
x
x
x
. (ii) Show that
x
2
−
4
x^2-4
x
2
−
4
is a factor of
f
(
x
)
f(x)
f
(
x
)
. (iii) Factorise
f
(
x
)
f(x)
f
(
x
)
completely and list all of its zeros.
Related theory
Polynomials
Factorisation of Polynomials
Polynomial Functions
Algebra
Solving quadratic equations
Browse the problem library