Home
::
About Us
::
Tutor in Your Home
::
Tutoring Center
::
SUMMER CAMP
::
Advertise With Us
::
College Counseling
::
Contact Us
Math is Fun
This site is an online mathematics and science school
where you can study without leaving your home (online education).
"
Do not worry about your difficulties in mathematics, I assure you that mine are greater
". Einstein, Albert (1879-1955)
Login
::
Sign Up - FREE
::
Refer a Friend
Study Guide
School of Logical Thinking
Tests Examples - Demo
Elementary Mathematics
High School Placement
Placement College Test
ACT
SAT
Flash Games
ACT
ACT Assessment
Test Description
English Test
Mathematics Test
Reading Test
Science Test
Writing Test
SAT
Early Mathematics
Study Guide
Arithmetic
Algebra
Geometry
Trigonometry
Divisibility of binomials
As consequences from Bezout’s theorem the next criteria of divisibility of binomials are valid:
1) A difference of identical powers of two numbers is divided without a remainder by a difference of these two numbers,
i.e. x
^{m}
– a
^{m}
is divided by x – a.
2) A difference of identical even powers of two numbers is divided without a remainder both by a difference and by a sum of these two numbers, i.e. if m – an even number, then the binomial
x
^{m}
– a
^{m}
is divided both by x – a and by x + a.
A difference of identical odd powers of two numbers isn’t divided by a sum of these two numbers.
3) A sum of identical powers of two numbers is never divided by a difference of these two numbers.
4) A sum of identical odd powers of two numbers is divided without a remainder by a sum of these two numbers.
5) A sum of identical even powers of two numbers is never divided both by difference and by a sum of these two numbers.
Example:
( x
^{2}
– a
^{2}
) : ( x – a ) = x + a ;
( x
^{3}
– a
^{3}
) : ( x – a ) = x
^{2}
+ a x+ a
^{2}
;
( x
^{5}
– a
^{5}
) : ( x – a ) = x
^{4}
+ a x
^{3}
+ a
^{2}
x
^{2}
+ a
^{3}
x + a
^{4}
.
Return Back
View My Stats
Privacy Statement
© 2006 MathPlusFun, All Rights Reserved