To find the difference between the polynomials [tex]\((9x^2 + 8x)\)[/tex] and [tex]\((2x^2 + 3x)\)[/tex], we need to subtract the corresponding coefficients of like terms. Here is the step-by-step process:
1. Identify the coefficients of the corresponding terms in each polynomial:
- For [tex]\(x^2\)[/tex], the coefficients are 9 from [tex]\((9x^2 + 8x)\)[/tex] and 2 from [tex]\((2x^2 + 3x)\)[/tex].
- For [tex]\(x\)[/tex], the coefficients are 8 from [tex]\((9x^2 + 8x)\)[/tex] and 3 from [tex]\((2x^2 + 3x)\)[/tex].
2. Subtract the coefficients of the like terms:
- For the [tex]\(x^2\)[/tex] terms:
[tex]\[
9x^2 - 2x^2 = (9 - 2)x^2 = 7x^2
\][/tex]
- For the [tex]\(x\)[/tex] terms:
[tex]\[
8x - 3x = (8 - 3)x = 5x
\][/tex]
3. Combine the results of the subtractions:
[tex]\[
7x^2 + 5x
\][/tex]
Therefore, the difference between the polynomials [tex]\((9x^2 + 8x)\)[/tex] and [tex]\((2x^2 + 3x)\)[/tex] is [tex]\(\boxed{7x^2 + 5x}\)[/tex].
Among the provided options, the correct one is:
[tex]\[
7 x^2 + 5 x
\][/tex]
