Question

"Name the polynomial by degree and number of terms.

3x^5 - 2x^4 + x^3 + 4x^2 - x + 4
Subtract:
(5x^2 - 2x + 6) - (-8x^2 + 3x^2 - 1)"

Answer 1

A fifth-degree polynomial with six terms is known as a hexanomial. The subtraction (5x^2 - 2x + 6) - (-8x^2 + 3x^2 - 1) results in the quadratic function 13x^2 - 2x + 7.

Step-by-step explanation:

The polynomial given in the question is 3x^5 - 2x^4 + x^3 + 4x^2 - x + 4. To name the polynomial by degree and number of terms, we must identify the highest power of x, which is 5 in this case. Thus, the polynomial is a fifth-degree polynomial, and since it has six terms, it is also referred to as a hexanomial.

To perform the subtraction (5x^2 - 2x + 6) - (-8x^2 + 3x^2 - 1), we simplify the expression by combining like terms:

1. First, distribute the negative sign through the second set of parentheses to get 5x^2 - 2x + 6 + 8x^2 - 3x^2 + 1.
2. Next, combine like terms to simplify the polynomial: (13x^2 - 2x + 7).

The result of the subtraction is another polynomial, 13x^2 - 2x + 7, which is a second-degree polynomial or a quadratic function.