To find the sum of the given polynomials [tex]\((x^2 - 3x) + (-2x^2 + 5x - 3)\)[/tex], we need to add the corresponding coefficients of the like terms.
### Step 1: Write down the polynomials
The given polynomials are:
[tex]\[ P_1(x) = x^2 - 3x \][/tex]
[tex]\[ P_2(x) = -2x^2 + 5x - 3 \][/tex]
### Step 2: Identify and organize the like terms
We need to combine like terms for [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant term.
### Step 3: Add the coefficients of the like terms
1. For [tex]\(x^2\)[/tex] term:
[tex]\[ 1x^2 + (-2x^2) = x^2 - 2x^2 = -x^2 \][/tex]
2. For [tex]\(x\)[/tex] term:
[tex]\[ -3x + 5x = 2x \][/tex]
3. For the constant term:
[tex]\[ 0 + (-3) = -3 \][/tex]
### Step 4: Combine the results
Combining these results gives us the sum of the polynomials in standard form:
[tex]\[ -x^2 + 2x - 3 \][/tex]
### Final Answer:
The sum of the given polynomials in standard form is:
[tex]\[ \boxed{-x^2 + 2x - 3} \][/tex]
So the correct option is:
[tex]\[ \boxed{-x^2 + 2x - 3} \][/tex]
