Consider the following polynomial functions: f(a)=(2a-7+a^2) and g(a)=(5-a)
Which of the following statements about the polynomial functions are true? Select all that apply
The expression that represents the sum of the polynomials is a first-degree polynomial.
The expression that represents the difference of the polynomials illustrates that polynomials are closed under subtraction.
The sum of f(a) and g(a) can be represented by the expression a^2 + a - 2
The difference of f(a) and g(a) can be represented by the expression a^2 + a - 12
The product of f(a) and g(a) can be represented by the expression -a^3 + 3a^2 + 17a - 35
The statements that are true are:
- The expression that represents the sum of the polynomials is a first-degree polynomial.
- The expression that represents the difference of the polynomials illustrates that polynomials are closed under subtraction.
Are you sure?
I apologize for the mistake. Let's go through each statement again:
1. The expression that represents the sum of the polynomials is a first-degree polynomial.
- This statement is false because the sum of the two polynomials would result in a second-degree polynomial, so this statement is incorrect.
2. The expression that represents the difference of the polynomials illustrates that polynomials are closed under subtraction.
- This statement is true. The difference of two polynomials always results in another polynomial, demonstrating closure under subtraction.
3. The sum of f(a) and g(a) can be represented by the expression a^2 + a - 2.
- This statement is false. The sum of the two given polynomials results in a^2 - 2a - 2, not a^2 + a - 2.
4. The difference of f(a) and g(a) can be represented by the expression a^2 + a - 12.
- This statement is false. The difference of the two given polynomials results in a^2 + 3a - 2, not a^2 + a - 12.
5. The product of f(a) and g(a) can be represented by the expression -a^3 + 3a^2 + 17a - 35.
- This statement is false. The product of the two given polynomials results in a^3 - 7a^2 - 44a + 35, not -a^3 + 3a^2 + 17a - 35.
Therefore, the correct statements are:
- The expression that represents the difference of the polynomials illustrates that polynomials are closed under subtraction.