Answer :
To identify the degree of the polynomial [tex]\( y = 2x^5 - 5x^4 - 30x^3 + 5x^2 + 88x + 60 \)[/tex], follow these steps:
1. Understand the Structure of a Polynomial:
A polynomial is composed of terms. Each term consists of a coefficient (a number) multiplied by a variable raised to an exponent (a power).
2. Identify the Degree:
The degree of a polynomial is the highest exponent of the variable [tex]\( x \)[/tex] in the polynomial.
3. Examine Each Term:
Let's look at each term in the polynomial:
- The term [tex]\( 2x^5 \)[/tex] has an exponent of 5.
- The term [tex]\( -5x^4 \)[/tex] has an exponent of 4.
- The term [tex]\( -30x^3 \)[/tex] has an exponent of 3.
- The term [tex]\( 5x^2 \)[/tex] has an exponent of 2.
- The term [tex]\( 88x \)[/tex] has an exponent of 1.
- The constant term [tex]\( 60 \)[/tex] can be considered as [tex]\( 60x^0 \)[/tex], with an exponent of 0.
4. Find the Highest Exponent:
Among the exponents [tex]\(5, 4, 3, 2, 1, 0\)[/tex], the highest is 5.
5. Conclusion:
The degree of the polynomial is the highest exponent, which is 5.
Thus, the degree of the polynomial [tex]\( y = 2x^5 - 5x^4 - 30x^3 + 5x^2 + 88x + 60 \)[/tex] is 5.
1. Understand the Structure of a Polynomial:
A polynomial is composed of terms. Each term consists of a coefficient (a number) multiplied by a variable raised to an exponent (a power).
2. Identify the Degree:
The degree of a polynomial is the highest exponent of the variable [tex]\( x \)[/tex] in the polynomial.
3. Examine Each Term:
Let's look at each term in the polynomial:
- The term [tex]\( 2x^5 \)[/tex] has an exponent of 5.
- The term [tex]\( -5x^4 \)[/tex] has an exponent of 4.
- The term [tex]\( -30x^3 \)[/tex] has an exponent of 3.
- The term [tex]\( 5x^2 \)[/tex] has an exponent of 2.
- The term [tex]\( 88x \)[/tex] has an exponent of 1.
- The constant term [tex]\( 60 \)[/tex] can be considered as [tex]\( 60x^0 \)[/tex], with an exponent of 0.
4. Find the Highest Exponent:
Among the exponents [tex]\(5, 4, 3, 2, 1, 0\)[/tex], the highest is 5.
5. Conclusion:
The degree of the polynomial is the highest exponent, which is 5.
Thus, the degree of the polynomial [tex]\( y = 2x^5 - 5x^4 - 30x^3 + 5x^2 + 88x + 60 \)[/tex] is 5.
