Certainly! Let's add the given polynomials step-by-step:
The given polynomials are:
[tex]\[P_1(x) = x^2 - 3x\][/tex]
[tex]\[P_2(x) = -2x^2 + 5x - 3\][/tex]
To find the sum, we add the corresponding coefficients of each polynomial.
1. Add the \(x^2\) terms:
[tex]\[
1x^2 + (-2x^2) = 1 - 2 = -1x^2
\][/tex]
2. Add the \(x\) terms:
[tex]\[
-3x + 5x = 5 - 3 = 2x
\][/tex]
3. Add the constant terms:
[tex]\[
0 + (-3) = -3
\][/tex]
Putting it all together, we get the resulting polynomial:
[tex]\[
-x^2 + 2x - 3
\][/tex]
Therefore, the sum of the given polynomials in standard form is:
[tex]\[
-x^2 + 2x - 3
\][/tex]
Hence, the correct answer from the given options is:
[tex]\[
-x^2 + 2x - 3
\][/tex]
