High School

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What is the leading term of the following polynomial?

\[ x^3 + 10x - 2x^6 + 12 \]

A. \( x^3 \)
B. \(-2x^6 \)
C. \(2x^6 \)
D. 12

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].

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