Answer:
The two correct options, to correct Martha's homework assignment are fhe first and the second:
- The first term, 5x³, can be eliminated, and
- The exponent of the first term, 5x³, can be changed to a 2 and then combined with the second term, 2x².
Explanation:
The function she wrote is f(x) = 5x³ + 2x² + 7x - 3.
That is not a quadratic function but a cubic function.
A quadratic function is a polynomial of degree two (the highest exponent of the variable is 2), while in the given function, 5x³ + 2x² + 7x - 3, the highest exponent of the variable is three (meaning it is a polynomial of degree 3).
Then, to change the function f(x) = 5x³ + 2x² + 7x - 3 to a degree two polynomial (quadratic function) you must eliminate any term where the variable, x, appears raised to a power greater than 2.
The only term with the variable, x, raised to a power greater than 2 is 5x³, so what she must do is to eliminate that term or change the exponent.
By eliminating the term 5x³ she will get the new polynomial 2x² + 7x - 3, whose highest power is 2, being a quadratic function as desired.
By changing the exponent of the first term, 5x³, to a 2, she will get the new polynomial 5x² + 2x² + 7x - 3. In such polynomial, 5x² and 2x² are like terms, so they can be combined to obtain 7x² + 7x - 3, which is a quadratic function, as desired.
