Sure! Let's find the sum of the given polynomials step by step.
First, we note the given polynomials:
1. [tex]\( x^2 - 3x \)[/tex]
2. [tex]\( -2x^2 + 5x - 3 \)[/tex]
We'll add the corresponding coefficients of each term from both polynomials:
### Step 1: Combine the [tex]\( x^2 \)[/tex] terms:
- From the first polynomial: [tex]\( 1 \cdot x^2 \)[/tex]
- From the second polynomial: [tex]\( -2 \cdot x^2 \)[/tex]
Adding these coefficients:
[tex]\[ 1 + (-2) = -1 \][/tex]
So, for the [tex]\( x^2 \)[/tex] term, we have:
[tex]\[ -1 \cdot x^2 \][/tex]
### Step 2: Combine the [tex]\( x \)[/tex] terms:
- From the first polynomial: [tex]\( -3 \cdot x \)[/tex]
- From the second polynomial: [tex]\( 5 \cdot x \)[/tex]
Adding these coefficients:
[tex]\[ -3 + 5 = 2 \][/tex]
So, for the [tex]\( x \)[/tex] term, we have:
[tex]\[ 2 \cdot x \][/tex]
### Step 3: Combine the constant terms:
- From the first polynomial: There is no constant term, so this is 0.
- From the second polynomial: [tex]\( -3 \)[/tex]
Adding these coefficients:
[tex]\[ 0 + (-3) = -3 \][/tex]
So, for the constant term, we have:
[tex]\[ -3 \][/tex]
### Combining all the terms:
Putting the combined terms together, we get the resulting polynomial:
[tex]\[ -1 \cdot x^2 + 2 \cdot x - 3 \][/tex]
Or simply:
[tex]\[ -x^2 + 2x - 3 \][/tex]
Thus, the sum of the given polynomials in standard form is:
[tex]\[ \boxed{ -x^2 + 2x - 3 } \][/tex]
