To find the difference of the two polynomials [tex]\((9x^2 + 8x)\)[/tex] and [tex]\((2x^2 + 3x)\)[/tex], we will subtract the corresponding coefficients of the terms.
1. Subtract the [tex]\(x^2\)[/tex] terms:
[tex]\[
9x^2 - 2x^2 = (9 - 2)x^2 = 7x^2
\][/tex]
2. Subtract the [tex]\(x\)[/tex] terms:
[tex]\[
8x - 3x = (8 - 3)x = 5x
\][/tex]
3. The resulting polynomial after subtraction is:
[tex]\[
7x^2 + 5x
\][/tex]
Therefore, the difference of the two polynomials [tex]\((9x^2 + 8x) - (2x^2 + 3x)\)[/tex] is:
[tex]\[
7x^2 + 5x
\][/tex]
From the given options, the correct answer is:
[tex]\[
7x^2 + 5x
\][/tex]
