Final answer:
The polynomial x⁴ + 3x² - x is a quartic trinomial since it has a degree of 4 and consists of three terms. n general, the term quadratic polynomial refers to a second-degree polynomial, a cubic polynomial to a third-degree polynomial, and a quadratic equation takes the form ax² + bx + c = 0, which can be solved using the quadratic formula.
Step-by-step explanation:
The polynomial x⁴ + 3x² - x should be named considering its degree and the number of terms it contains.
The degree of a polynomial is determined by the highest power of the variable, which in this case is 4 (the exponent on x⁴). A polynomial with a degree of 4 is called quartic.
The number of terms in the polynomial is 3 (x⁴, 3x², and -x), which makes it a trinomial. Hence, the correct name for this polynomial is a quartic trinomial.
In general, the term quadratic polynomial refers to a second-degree polynomial, a cubic polynomial to a third-degree polynomial, and a quadratic equation takes the form ax² + bx + c = 0, which can be solved using the quadratic formula.