Let's analyze the expression step-by-step:
### The Expression: [tex]\(\frac{1}{2} x^2 + x + 7\)[/tex]
This is a polynomial expression with three terms.
1. Number of Terms:
To determine the number of terms in the expression, we count the distinct parts separated by the addition ([tex]\(+\)[/tex]) or subtraction ([tex]\(-\)[/tex]) symbols:
- [tex]\(\frac{1}{2} x^2\)[/tex] is the first term.
- [tex]\(x\)[/tex] is the second term.
- [tex]\(7\)[/tex] is the third term.
Therefore, the entire expression is a sum with three terms.
2. Coefficients:
The coefficients are the numerical factors of each term:
- For the term [tex]\(\frac{1}{2} x^2\)[/tex], the coefficient is [tex]\(\frac{1}{2}\)[/tex].
- For the term [tex]\(x\)[/tex], the coefficient is [tex]\(1\)[/tex]; this is understood because [tex]\(x\)[/tex] is the same as [tex]\(1 \cdot x\)[/tex].
- For the constant term [tex]\(7\)[/tex], the "coefficient" can be considered [tex]\(7\)[/tex] itself as it effectively represents [tex]\(7 \cdot x^0\)[/tex] with [tex]\(x^0 = 1\)[/tex].
So, the coefficients are [tex]\([0.5, 1, 7]\)[/tex].
### Summary
1. The entire expression is a sum with three terms.
2. The coefficients are [tex]\[0.5, 1, 7\][/tex].
