Classify this polynomial: $-6 s^2+13$
A. fourth degree trinomial
B. cubic monomial
C. quadratic binomial
D. linear trinomial
Answer (2)
The polynomial − 6 s 2 + 13 has a degree of 2, making it a quadratic.
It has two terms, − 6 s 2 and 13 , making it a binomial.
Therefore, the polynomial is classified as a quadratic binomial.
The final answer is quadratic binomial q u a d r a t i c bin o mia l .
Explanation
Understanding the Polynomial We are asked to classify the polynomial − 6 s 2 + 13 . 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. In the polynomial − 6 s 2 + 13 , the variable is s , and its highest power is 2. Therefore, the degree of the polynomial is 2. A polynomial of degree 2 is called a quadratic polynomial.
Counting the Terms The terms of a polynomial are the parts separated by addition or subtraction. In the polynomial − 6 s 2 + 13 , there are two terms: − 6 s 2 and 13 . A polynomial with two terms is called a binomial.
Classification Since the polynomial has a degree of 2 and two terms, it is a quadratic binomial.
Examples
Understanding polynomial classification is crucial in various fields, such as physics and engineering, where mathematical models often involve polynomials. For instance, the trajectory of a projectile can be modeled using a quadratic polynomial, and classifying this polynomial helps in predicting the projectile's path and landing point. Similarly, in signal processing, polynomials are used to represent and analyze signals, and their classification aids in designing filters and other signal processing algorithms. By mastering polynomial classification, students gain a foundational skill that enables them to tackle real-world problems in diverse scientific and technological domains.
The polynomial − 6 s 2 + 13 is classified as a quadratic binomial because it has a degree of 2 and consists of two terms. Therefore, the correct answer is option C: quadratic binomial.
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