To find the sum of the given polynomials \( (3x^2 + x - 7) + (-5x^2 + x - 3) \), we need to add the corresponding coefficients of \( x^2 \), \( x \), and the constant terms.
Let's break it down step-by-step:
1. Identify the coefficients from each polynomial:
- For the first polynomial \( 3x^2 + x - 7 \):
- Coefficient of \( x^2 \): 3
- Coefficient of \( x \): 1
- Constant term: -7
- For the second polynomial \( -5x^2 + x - 3 \):
- Coefficient of \( x^2 \): -5
- Coefficient of \( x \): 1
- Constant term: -3
2. Add the coefficients of \( x^2 \):
[tex]\[
3 + (-5) = -2
\][/tex]
So, the coefficient of \( x^2 \) in the sum is \( -2 \).
3. Add the coefficients of \( x \):
[tex]\[
1 + 1 = 2
\][/tex]
So, the coefficient of \( x \) in the sum is \( 2 \).
4. Add the constant terms:
[tex]\[
-7 + (-3) = -10
\][/tex]
So, the constant term in the sum is \( -10 \).
Therefore, the sum of the polynomials \( (3x^2 + x -7) + (-5x^2 + x - 3) \) is:
[tex]\[
\boxed{-2x^2 + 2x - 10}
\][/tex]
