To find the difference between the two polynomials [tex]\((9x^2 + 8x)\)[/tex] and [tex]\((2x^2 + 3x)\)[/tex], we perform the following steps:
1. Align the terms based on their degrees:
- The first polynomial is [tex]\(9x^2 + 8x\)[/tex].
- The second polynomial is [tex]\(2x^2 + 3x\)[/tex].
2. Subtract the corresponding coefficients:
- Subtract the coefficient of [tex]\(x^2\)[/tex] in the second polynomial from the coefficient of [tex]\(x^2\)[/tex] in the first polynomial:
[tex]\[
9 - 2 = 7
\][/tex]
- Subtract the coefficient of [tex]\(x\)[/tex] in the second polynomial from the coefficient of [tex]\(x\)[/tex] in the first polynomial:
[tex]\[
8 - 3 = 5
\][/tex]
3. Form the new polynomial with the resulting coefficients:
- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(7\)[/tex].
- The coefficient of [tex]\(x\)[/tex] is [tex]\(5\)[/tex].
Thus, the difference of the two polynomials is:
[tex]\[
7x^2 + 5x
\][/tex]
Among the given options, the correct answer is:
[tex]\[
\boxed{7x^2 + 5x}
\][/tex]
