To subtract the given polynomials [tex]\((4x^2 - x + 6) - (x^2 + 3)\)[/tex], let's go through the operation step by step.
### Step 1: Write Down the Polynomials
The first polynomial is:
[tex]\[4x^2 - x + 6\][/tex]
The second polynomial is:
[tex]\[x^2 + 3\][/tex]
### Step 2: Subtraction of Corresponding Terms
We'll subtract the second polynomial from the first polynomial by subtracting corresponding terms.
1. Subtract the [tex]\(x^2\)[/tex] terms:
[tex]\[4x^2 - x^2\][/tex]
Simplifies to:
[tex]\[3x^2\][/tex]
2. Subtract the [tex]\(x\)[/tex] terms:
Here, the first polynomial has a [tex]\(-x\)[/tex] term and the second polynomial does not have an [tex]\(x\)[/tex] term. So:
[tex]\[-x - 0\][/tex]
Simplifies to:
[tex]\[-x\][/tex]
3. Subtract the constant terms:
[tex]\[6 - 3\][/tex]
Simplifies to:
[tex]\[3\][/tex]
### Step 3: Combine the Results
Combining the results from each step, we get:
[tex]\[3x^2 - x + 3\][/tex]
### Step 4: Match with the Given Options
Now let's match this result with the provided options.
A. [tex]\(3x^2 - x + 3\)[/tex]
B. [tex]\(5x^2 - x + 9\)[/tex]
C. [tex]\(4x^2 - 2x + 9\)[/tex]
D. [tex]\(4x^2 - 2x + 3\)[/tex]
The correct matching option is:
A. [tex]\(3x^2 - x + 3\)[/tex]
### Final Answer
Therefore, the result of the subtraction [tex]\((4x^2 - x + 6) - (x^2 + 3)\)[/tex] is:
[tex]\[ \boxed{3x^2 - x + 3} \][/tex]
So, the correct option is:
[tex]\[ A. 3x^2 - x + 3 \][/tex]
