Certainly! Let's combine the like terms from the given polynomials step by step:
Given expression:
[tex]\[ 6x^2 - 5x + 12 + 3x^2 + 4x - 7 \][/tex]
1. Group like terms together:
[tex]\[ (6x^2 + 3x^2) + (-5x + 4x) + (12 - 7) \][/tex]
2. Combine the coefficients of [tex]\(x^2\)[/tex]:
[tex]\[ 6x^2 + 3x^2 = 9x^2 \][/tex]
3. Combine the coefficients of [tex]\(x\)[/tex]:
[tex]\[ -5x + 4x = -1x \][/tex]
4. Combine the constant terms:
[tex]\[ 12 - 7 = 5 \][/tex]
So, when we combine like terms, we get:
[tex]\[ 9x^2 - 1x + 5 \][/tex]
Thus, the result is:
[tex]\[ 9x^2 - x + 5 \][/tex]
