Answer :
To find the leading term of a polynomial, we need to identify the term with the highest degree (or exponent) of the variable.
The polynomial in question is:
[tex]\[ x^3 + 10x - 2x^6 + 12 \][/tex]
Step-by-step solution:
1. Identify Each Term and Its Degree:
- [tex]\( x^3 \)[/tex]: The degree is 3
- [tex]\( 10x \)[/tex]: The degree is 1
- [tex]\( -2x^6 \)[/tex]: The degree is 6
- [tex]\( 12 \)[/tex]: The degree is 0 (since it's a constant)
2. Determine the Highest Degree:
The term with the highest degree determines the leading term. Here, the highest degree is 6.
3. Identify the Term with the Highest Degree:
The term with the degree of 6 is [tex]\( -2x^6 \)[/tex].
4. Conclusion:
The leading term of the polynomial is [tex]\( -2x^6 \)[/tex].
Thus, the correct answer is (2) [tex]\( -2x^6 \)[/tex].
The polynomial in question is:
[tex]\[ x^3 + 10x - 2x^6 + 12 \][/tex]
Step-by-step solution:
1. Identify Each Term and Its Degree:
- [tex]\( x^3 \)[/tex]: The degree is 3
- [tex]\( 10x \)[/tex]: The degree is 1
- [tex]\( -2x^6 \)[/tex]: The degree is 6
- [tex]\( 12 \)[/tex]: The degree is 0 (since it's a constant)
2. Determine the Highest Degree:
The term with the highest degree determines the leading term. Here, the highest degree is 6.
3. Identify the Term with the Highest Degree:
The term with the degree of 6 is [tex]\( -2x^6 \)[/tex].
4. Conclusion:
The leading term of the polynomial is [tex]\( -2x^6 \)[/tex].
Thus, the correct answer is (2) [tex]\( -2x^6 \)[/tex].
