Consider the following polynomial: -9 + x4 – 5x + 2×3 + 5x This polynomial can be classified as fifth degree. fourth degree. monomial. binomial. trinomial.
The Correct Answer and Explanation is:
Correct Answer: Fourth degree trinomial
Explanation:
To classify the polynomial, we need to follow these steps:
Step 1: Combine like terms and arrange in standard form
The given polynomial is: −9+x4−5x+2×3+5x-9 + x^4 – 5x + 2x^3 + 5x−9+x4−5x+2×3+5x
First, combine like terms. Notice that -5x and +5x cancel each other out: −9+x4+2×3-9 + x^4 + 2x^3−9+x4+2×3
Now arrange in descending order of exponents: x4+2×3−9x^4 + 2x^3 – 9×4+2×3−9
Step 2: Determine the degree
The degree of a polynomial is the highest power of the variable. In this simplified expression: x4+2×3−9x^4 + 2x^3 – 9×4+2×3−9
The highest exponent is 4, from the term x⁴, so the degree is 4. Therefore, the polynomial is classified as a fourth-degree polynomial.
Step 3: Count the number of terms
A polynomial’s type can also be described by the number of non-zero terms:
- Monomial: 1 term
- Binomial: 2 terms
- Trinomial: 3 terms
The simplified version has three terms:
- x4x^4×4
- 2x32x^32×3
- −9-9−9
So, the polynomial is a trinomial.
Conclusion
Putting the classification together:
- The degree is 4
- There are 3 terms
Thus, the polynomial is a fourth-degree trinomial.
This classification helps in understanding the behavior of the polynomial, especially when graphing or solving. Higher-degree polynomials can have more turning points, and identifying the number of terms simplifies factoring and operations.
