To find the leading coefficient and the degree of the polynomial [tex]\( 2 + 7x - 12x^5 - 2x^9 \)[/tex], we need to follow these steps:
1. Identify the Degree of Each Term:
- For the constant term [tex]\( 2 \)[/tex], the degree is 0.
- For the term [tex]\( 7x \)[/tex], the degree is 1.
- For the term [tex]\( -12x^5 \)[/tex], the degree is 5.
- For the term [tex]\( -2x^9 \)[/tex], the degree is 9.
2. Determine the Highest Degree:
- The degrees in the polynomial are 0, 1, 5, and 9.
- The highest degree among these is 9.
3. Find the Leading Coefficient:
- The leading coefficient is the coefficient of the term with the highest degree.
- The term with the highest degree [tex]\( 9 \)[/tex] is [tex]\( -2x^9 \)[/tex].
- Therefore, the leading coefficient is [tex]\( -2 \)[/tex].
Thus, the leading coefficient is [tex]\( -2 \)[/tex] and the degree of the polynomial is [tex]\( 9 \)[/tex].
