To find the sum of the given polynomials [tex]\((x^2 - 3x)\)[/tex] and [tex]\((-2x^2 + 5x - 3)\)[/tex], we need to add their corresponding coefficients.
### Step-by-Step Solution
1. Identify and align the coefficients of corresponding terms:
For the polynomial [tex]\(x^2 - 3x\)[/tex], we can consider it as:
[tex]\[1x^2 + (-3)x + 0\][/tex]
For the polynomial [tex]\(-2x^2 + 5x - 3\)[/tex], we have:
[tex]\[-2x^2 + 5x - 3\][/tex]
2. Add the coefficients of like terms:
- Constant term:
[tex]\[0 + (-3) = -3\][/tex]
- Linear term (x):
[tex]\[-3 + 5 = 2\][/tex]
- Quadratic term (x^2):
[tex]\[1 + (-2) = -1\][/tex]
3. Combine these results to form the polynomial in standard form:
[tex]\[
-1x^2 + 2x - 3
\][/tex]
So, the sum of the polynomials [tex]\((x^2 - 3x) + (-2x^2 + 5x - 3)\)[/tex] in standard form is:
[tex]\[
-1x^2 + 2x - 3
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-x^2 + 2x - 3}
\][/tex]
