Answer :
Certainly! Let's find the degree of the polynomial [tex]\(25x^3 + 12x^2 - x\)[/tex].
The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] that has a non-zero coefficient. Here's how to determine it step-by-step:
1. Identify each term in the polynomial:
- [tex]\(25x^3\)[/tex]
- [tex]\(12x^2\)[/tex]
- [tex]\(-x\)[/tex]
2. Look at the exponent (power) of the variable [tex]\(x\)[/tex] in each term:
- In [tex]\(25x^3\)[/tex], the power of [tex]\(x\)[/tex] is 3.
- In [tex]\(12x^2\)[/tex], the power of [tex]\(x\)[/tex] is 2.
- In [tex]\(-x\)[/tex], the power of [tex]\(x\)[/tex] is 1.
3. The degrees we've found are 3, 2, and 1 for each term, respectively.
4. The degree of the polynomial is the highest one among these powers. So, we take the maximum value from 3, 2, and 1.
Thus, the degree of the polynomial [tex]\(25x^3 + 12x^2 - x\)[/tex] is 3.
The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] that has a non-zero coefficient. Here's how to determine it step-by-step:
1. Identify each term in the polynomial:
- [tex]\(25x^3\)[/tex]
- [tex]\(12x^2\)[/tex]
- [tex]\(-x\)[/tex]
2. Look at the exponent (power) of the variable [tex]\(x\)[/tex] in each term:
- In [tex]\(25x^3\)[/tex], the power of [tex]\(x\)[/tex] is 3.
- In [tex]\(12x^2\)[/tex], the power of [tex]\(x\)[/tex] is 2.
- In [tex]\(-x\)[/tex], the power of [tex]\(x\)[/tex] is 1.
3. The degrees we've found are 3, 2, and 1 for each term, respectively.
4. The degree of the polynomial is the highest one among these powers. So, we take the maximum value from 3, 2, and 1.
Thus, the degree of the polynomial [tex]\(25x^3 + 12x^2 - x\)[/tex] is 3.
