The difference between the polynomials, [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex] is expressed as: [tex]\mathbf{2x^3 + 2x}[/tex]
Given the polynomials:
- [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex],
We are required to find their difference which can be solved as follows:
[tex](x^4 + x^3 + x^2 + x ) - ( x^4 - x^3 + x^2 - x)[/tex]
First, open the bracket by multiplying every term you have in [tex]( x^4 - x^3 + x^2 - x)[/tex] by -1:
[tex]x^4 + x^3 + x^2 + x - x^4 + x^3 - x^2 + x[/tex]
- Group like terms together and add them together
[tex]x^4 - x^4 + x^3 + x^3 + x^2 - x^2 + x + x\\\\\mathbf{2x^3 + 2x}[/tex]
Thus, the difference between the polynomials, [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex] is expressed as: [tex]\mathbf{2x^3 + 2x}[/tex]
Learn more here:
https://brainly.com/question/9351663
