Answer :
Let’s complete the following polynomial expression:
[tex]\[ x^2 + \frac{1}{2}x - 4 \][/tex]
### Step-by-Step Solution:
1. Identify the polynomial's general form.
The given expression [tex]\( x^2 + \frac{1}{2}x - 4 \)[/tex] is a quadratic polynomial of the form [tex]\( ax^2 + bx + c \)[/tex], where:
[tex]\[ a = 1, \quad b = \frac{1}{2}, \quad c = -4 \][/tex]
2. Verify by rewriting the polynomial.
To ensure clarity, let's rewrite the polynomial in its standard form:
[tex]\[ x^2 + 0.5x - 4 \][/tex]
3. Understanding the structure:
- The quadratic term is [tex]\( x^2 \)[/tex]
- The linear term is [tex]\( 0.5x \)[/tex]
- The constant term is [tex]\(-4\)[/tex]
This is the complete form of the quadratic polynomial. We have now verified the structure of the polynomial, and it is given that
[tex]\[ \boxed{x^2 + 0.5x - 4} \][/tex]
This completes interpreting the given polynomial and ensuring its correctness.
[tex]\[ x^2 + \frac{1}{2}x - 4 \][/tex]
### Step-by-Step Solution:
1. Identify the polynomial's general form.
The given expression [tex]\( x^2 + \frac{1}{2}x - 4 \)[/tex] is a quadratic polynomial of the form [tex]\( ax^2 + bx + c \)[/tex], where:
[tex]\[ a = 1, \quad b = \frac{1}{2}, \quad c = -4 \][/tex]
2. Verify by rewriting the polynomial.
To ensure clarity, let's rewrite the polynomial in its standard form:
[tex]\[ x^2 + 0.5x - 4 \][/tex]
3. Understanding the structure:
- The quadratic term is [tex]\( x^2 \)[/tex]
- The linear term is [tex]\( 0.5x \)[/tex]
- The constant term is [tex]\(-4\)[/tex]
This is the complete form of the quadratic polynomial. We have now verified the structure of the polynomial, and it is given that
[tex]\[ \boxed{x^2 + 0.5x - 4} \][/tex]
This completes interpreting the given polynomial and ensuring its correctness.
