Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
AoPS
MATHEMATICS · Multi-part · AoPS · Mathematics · Polynomials · Polynomials
Problem
Let
p
(
x
)
=
3
x
3
−
2
x
2
+
5
x
−
7
p(x)=3x^{3}-2x^{2}+5x-7
p
(
x
)
=
3
x
3
−
2
x
2
+
5
x
−
7
and
q
(
x
)
=
−
x
3
+
4
x
−
9
q(x)=-x^{3}+4x-9
q
(
x
)
=
−
x
3
+
4
x
−
9
. (i) Find the polynomial
s
(
x
)
=
p
(
x
)
+
q
(
x
)
s(x)=p(x)+q(x)
s
(
x
)
=
p
(
x
)
+
q
(
x
)
and write it in descending powers of
x
x
x
. (ii) Find the polynomial
t
(
x
)
=
p
(
x
)
q
(
x
)
t(x)=p(x)\,q(x)
t
(
x
)
=
p
(
x
)
q
(
x
)
and simplify it completely. (iii) Calculate the value of
u
=
p
(
2
)
−
q
(
2
)
u=p(2)-q(2)
u
=
p
(
2
)
−
q
(
2
)
.
Related theory
Polynomials
Polynomial Functions
Polynomials in one variable
Browse the problem library