Answer :
To determine the leading term of the polynomial [tex]\(3 + 2x - 7x^3\)[/tex], we need to identify the term with the highest power of [tex]\(x\)[/tex].
Here's how you do it step-by-step:
1. Identify each term and its power of [tex]\(x\)[/tex]:
- The first term is [tex]\(3\)[/tex], which can be written as [tex]\(3x^0\)[/tex] (since any number to the power of zero is 1).
- The second term is [tex]\(2x\)[/tex], which is [tex]\(2x^1\)[/tex].
- The third term is [tex]\(-7x^3\)[/tex], which is [tex]\(-7x^3\)[/tex].
2. Compare the powers of [tex]\(x\)[/tex] in each term:
- The powers are 0 for the first term, 1 for the second term, and 3 for the third term.
3. Determine the term with the highest power of [tex]\(x\)[/tex]:
- The highest power is 3.
4. Identify the leading term:
- The term with the highest power is [tex]\(-7x^3\)[/tex].
Therefore, the leading term of the polynomial [tex]\(3 + 2x - 7x^3\)[/tex] is [tex]\(-7x^3\)[/tex].
Here's how you do it step-by-step:
1. Identify each term and its power of [tex]\(x\)[/tex]:
- The first term is [tex]\(3\)[/tex], which can be written as [tex]\(3x^0\)[/tex] (since any number to the power of zero is 1).
- The second term is [tex]\(2x\)[/tex], which is [tex]\(2x^1\)[/tex].
- The third term is [tex]\(-7x^3\)[/tex], which is [tex]\(-7x^3\)[/tex].
2. Compare the powers of [tex]\(x\)[/tex] in each term:
- The powers are 0 for the first term, 1 for the second term, and 3 for the third term.
3. Determine the term with the highest power of [tex]\(x\)[/tex]:
- The highest power is 3.
4. Identify the leading term:
- The term with the highest power is [tex]\(-7x^3\)[/tex].
Therefore, the leading term of the polynomial [tex]\(3 + 2x - 7x^3\)[/tex] is [tex]\(-7x^3\)[/tex].
