The sum of all three given polynomials evaluates to [tex]a + c + e[/tex]
How to do addition of polynomials?
When polynomials are added, the coefficients of like terms get added.
What are like terms?
Those terms which have same variables raised with same power.
For example, [tex]5t^3[/tex] and [tex]6t^3[/tex] are like terms since variable is same, and it is raised to same power 3.
For example [tex]x^3[/tex] and [tex]3x^4[/tex] are not like terms as the variables are same but powers aren't same.
What are coefficients?
Constants who are in multiplication with variables are called coefficients of those variables.
For example, in [tex]10x^2[/tex] we have 10 as coefficient of [tex]x^2[/tex]
Those variables who have got no visible coefficient has 1 as their coefficient. Thus, [tex]x^4[/tex] has got its coefficient as 1. It is true since 1 multiplied with any number is that number itself.
For the given condition, the three polynomials are added as:
[tex]\: \:\: \: a - b + c\\+b - c + d\\ + c - d + e\\\\ = a +b +c + (-b -c - d) + (c + d + e)\\ = a + (1-1)b + (1 -1 + 1)c +(-1 + 1)d + e\\= a + c + e[/tex]
Thus, the sum of all three given polynomials evaluates to [tex]a + c + e[/tex]
Learn more about addition of polynomials here:
https://brainly.com/question/14148883
