Classify this polynomial: [tex]5 x^3+17 x^2-1[/tex]
A. linear binomial
B. cubic monomial
C. cubic trinomial
D. constant
Answer (2)
Identify the degree of the polynomial as 3, classifying it as cubic.
Count the number of terms as 3, classifying it as a trinomial.
Combine the classifications to identify the polynomial as a cubic trinomial.
The final answer is cubic trinomial c u bi c t r in o mia l .
Explanation
Understanding the Polynomial We are given the polynomial 5 x 3 + 17 x 2 − 1 and asked to classify it. To do this, we need to determine its degree and the number of terms it has.
Determining the Degree The degree of a polynomial is the highest power of the variable x in the polynomial. In this case, the terms are 5 x 3 , 17 x 2 , and − 1 . The powers of x are 3, 2, and 0 (since − 1 = − 1 x 0 ). The highest power is 3, so the degree of the polynomial is 3. A polynomial of degree 3 is called a cubic polynomial.
Counting the Terms The number of terms in the polynomial is the number of distinct expressions that are added or subtracted. In this case, we have three terms: 5 x 3 , 17 x 2 , and − 1 . A polynomial with three terms is called a trinomial.
Final Classification Since the polynomial has degree 3 and three terms, it is a cubic trinomial.
Examples
Polynomials are used to model various real-world phenomena. For example, the trajectory of a projectile can be modeled using a quadratic polynomial. In economics, cost and revenue functions can often be expressed as polynomials. Understanding the classification of polynomials helps in choosing the appropriate model for a given situation.
The polynomial 5 x 3 + 17 x 2 − 1 is classified as a cubic trinomial because it has a degree of 3 and consists of three terms. The answer choice is C: cubic trinomial.
;
