Answer :
To find the leading coefficient of the polynomial expression [tex]\(18x^6 + x^3 - 7x^2 + 0.25\)[/tex], follow these steps:
1. Identify the term with the highest degree:
- The degree of a term is determined by the exponent of the variable [tex]\(x\)[/tex].
- Look at each term: [tex]\(18x^6\)[/tex], [tex]\(x^3\)[/tex], [tex]\(-7x^2\)[/tex], and [tex]\(0.25\)[/tex].
- The term [tex]\(18x^6\)[/tex] has the highest degree since the exponent 6 is the largest.
2. Find the coefficient of the term with the highest degree:
- In the term [tex]\(18x^6\)[/tex], the coefficient is the number that multiplies the variable, which is 18.
3. Determine the leading coefficient:
- The leading coefficient is the coefficient of the term with the highest degree.
- Therefore, the leading coefficient of the polynomial is 18.
So, the blank should be filled with 18.
1. Identify the term with the highest degree:
- The degree of a term is determined by the exponent of the variable [tex]\(x\)[/tex].
- Look at each term: [tex]\(18x^6\)[/tex], [tex]\(x^3\)[/tex], [tex]\(-7x^2\)[/tex], and [tex]\(0.25\)[/tex].
- The term [tex]\(18x^6\)[/tex] has the highest degree since the exponent 6 is the largest.
2. Find the coefficient of the term with the highest degree:
- In the term [tex]\(18x^6\)[/tex], the coefficient is the number that multiplies the variable, which is 18.
3. Determine the leading coefficient:
- The leading coefficient is the coefficient of the term with the highest degree.
- Therefore, the leading coefficient of the polynomial is 18.
So, the blank should be filled with 18.
