To determine the degree of the polynomial \( 2 - 6x + 7x^2 + 3x^3 - 3x^4 \), follow these steps:
1. Identify each term in the polynomial and their respective powers of \( x \):
- The term \( 2 \) has \( x^0 \) (since \( x^0 = 1 \)).
- The term \( -6x \) has \( x^1 \).
- The term \( 7x^2 \) has \( x^2 \).
- The term \( 3x^3 \) has \( x^3 \).
- The term \( -3x^4 \) has \( x^4 \).
2. List the exponents of \( x \) for each term:
- The exponents are \( 0, 1, 2, 3, \) and \( 4 \).
3. Determine the highest exponent:
- Among the exponents \( 0, 1, 2, 3, \) and \( 4 \), the highest is \( 4 \).
4. State the degree of the polynomial:
- The degree of a polynomial is defined as the highest power of \( x \) with a non-zero coefficient. Here, the term with the highest power is \( -3x^4 \), and its exponent is \( 4 \).
Therefore, the degree of the polynomial [tex]\( 2 - 6x + 7x^2 + 3x^3 - 3x^4 \)[/tex] is [tex]\( 4 \)[/tex].
