Long Division...3

[nycmathguy]

College Algebra
Chapter 1/Section 4

How is this done? Use LaTex or Wolfram. Thanks.

 

[MathLover1]

first factor (x^5-a^5)

then we have

 

[nycmathguy]

View attachment 3897

first factor (x^5-a^5)

View attachment 3898

then we have

View attachment 3899

View attachment 3900

Can you show the factor steps for x^5 - a^5?

 

[MathLover1]

Apply factoring rule :
x^n+y^n= (x+y ) (x^(n-1)-x^(n-2)y+...... -xy^(n-2)+y^(n-1)), where n is odd

 

[nycmathguy]

Apply factoring rule :
x^n+y^n= (x+y ) (x^(n-1)-x^(n-2)y+...... -xy^(n-2)+y^(n-1)), where n is odd

I would like to see the factoring work, if you don't mind.

 

[MathLover1]

just apply rule and and use n=5

x^5+a^5= (x+a ) (x^(5-1)a^(5-5) -x^(5-2)a^(5-4)+x^(5-3)a^(5-3)-x^(5-4)a^(5-2)+x^(5-5)a^(5-1))
x^5+a^5= (x+a ) (x^4a^0 -x^3a^1+x^2a^2-x^1a^3+x^0a^4)
x^5+a^5= (x+a ) (x^4 -x^3a+x^2a^2-xa^3+a^4)

 

[nycmathguy]

just apply rule and and use n=5

x^5+a^5= (x+a ) (x^(5-1)a^(5-5) -x^(5-2)a^(5-4)+x^(5-3)a^(5-3)-x^(5-4)a^(5-2)+x^(5-5)a^(5-1))
x^5+a^5= (x+a ) (x^4a^0 -x^3a^1+x^2a^2-x^1a^3+x^0a^4)
x^5+a^5= (x+a ) (x^4 -x^3a+x^2a^2-xa^3+a^4)

Interestingly difficult.