Sure! Let's subtract the polynomials step by step to obtain the answer.
Given the polynomials:
[tex]\[ 2x^2 + 5x - 10 \][/tex]
and
[tex]\[ 3x^2 - x + 9 \][/tex]
We need to subtract the second polynomial from the first polynomial. This means we need to perform:
[tex]\[ (2x^2 + 5x - 10) - (3x^2 - x + 9) \][/tex]
To make it simpler, let's distribute the negative sign through the second polynomial:
[tex]\[ 2x^2 + 5x - 10 - 3x^2 + x -9 \][/tex]
Now, combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(2x^2 - 3x^2 = -x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(5x + x = 6x\)[/tex]
- Combine the constant terms: [tex]\(-10 - 9 = -19\)[/tex]
Putting it all together, we get:
[tex]\[ -x^2 + 6x - 19 \][/tex]
So the result of the subtraction is:
[tex]\[ \boxed{-x^2 + 6x - 19} \][/tex]
