To subtract one polynomial from another, you subtract the corresponding coefficients of like terms. Let's follow through the steps for the given polynomials:
1. Identify the polynomials:
[tex]\[
\text{First polynomial: } -3x^2 + 10
\][/tex]
[tex]\[
\text{Second polynomial: } -2x^2 + 2
\][/tex]
2. Set up the subtraction:
[tex]\[
(-3x^2 + 10) - (-2x^2 + 2)
\][/tex]
3. Distribute the negative sign through the second polynomial:
[tex]\[
-3x^2 + 10 - (-2x^2) - 2
\][/tex]
[tex]\[
-3x^2 + 10 + 2x^2 - 2
\][/tex]
4. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-3x^2 + 2x^2 = -x^2
\][/tex]
- Combine the constant terms:
[tex]\[
10 - 2 = 8
\][/tex]
5. Write the final result:
[tex]\[
-x^2 + 8
\][/tex]
Therefore, the result of subtracting [tex]\(-2x^2 + 2\)[/tex] from [tex]\(-3x^2 + 10\)[/tex] is:
[tex]\[
8 - x^2
\][/tex]
