To subtract the given polynomials [tex]\((4x^2 - 3x + 8)\)[/tex] and [tex]\((2x^2 + 2x - 5)\)[/tex], we need to subtract the coefficients of the corresponding terms from each polynomial.
The first polynomial is:
[tex]\[ 4x^2 - 3x + 8 \][/tex]
The second polynomial is:
[tex]\[ 2x^2 + 2x - 5 \][/tex]
Step-by-step process:
1. Subtract the coefficients of [tex]\(x^2\)[/tex] terms:
[tex]\[ 4x^2 - 2x^2 = 2x^2 \][/tex]
2. Subtract the coefficients of [tex]\(x\)[/tex] terms:
[tex]\[ -3x - 2x = -5x \][/tex]
3. Subtract the constant terms:
[tex]\[ 8 - (-5) = 8 + 5 = 13 \][/tex]
Combining all these results, the polynomial obtained by subtraction is:
[tex]\[ 2x^2 - 5x + 13 \][/tex]
Therefore, the correct answer is:
[tex]\[ 2x^2 - 5x + 13 \][/tex]
So, the correct option is:
[tex]\[ \boxed{2 x^2 - 5 x + 13} \][/tex]
