Two examples of polynomial expressions are \(A(x) = 4x^5 - 3x^3 + 2x - 7\) (which is of degree 5) and \(B(x) = 2x^3 + 6x^2 + 1\) (which is of degree 3). When the two polynomials are added together to find their sum, we combine the like terms. The resulting polynomial is \[C(x) = A(x) + B(x) = 4x^5 + ( -3x^3 + 2x^3) + 6x^2 + (2x) - 7 + 1 = 4x^5 - x^3 + 6x^2 + 2x - 6.\] , and the highest degree term in this sum is \(4x^5\), which gives the polynomial \(C(x)\) a degree of 5.

Question

To find the first and last terms of a polynomial, we look for the leading term (the term with the highest exponent) and the constant term (the term without any variable). In standard polynomial form, this process is typically straightforward. However, if the polynomial is presented in a more complex or non-standard format, additional steps might be necessary to accurately identify the first and last terms.

rewrite this in first person.

Answer 1

Two examples of polynomial expressions that I have encountered are \(A(x) = 4x^5 - 3x^3 + 2x - 7\) (which is of degree 5) and \(B(x) = 2x^3 + 6x^2 + 1\) (which is of degree 3). When I add these two polynomials together to find their sum, I combine the like terms. The resulting polynomial is \[C(x) = A(x) + B(x) = 4x^5 + ( -3x^3 + 2x^3) + 6x^2 + (2x) - 7 + 1 = 4x^5 - x^3 + 6x^2 + 2x - 6.\]

In this process, I notice that the highest degree term in this sum is \(4x^5\), which gives the polynomial \(C(x)\) a degree of 5.

To find the first and last terms of a polynomial, I look for the leading term (the term with the highest exponent) and the constant term (the term without any variable). In standard polynomial form, I find this process to be typically straightforward. However, if the polynomial is presented in a more complex or non-standard format, I understand that additional steps might be necessary to accurately identify the first and last terms.