To find the product of the given polynomials, [tex]\((5x + 8 - 6x)(4 + 2x - 7)\)[/tex], we first simplify both polynomials, and then multiply them out.
1. Simplify the first polynomial:
[tex]\[
5x + 8 - 6x = (5x - 6x) + 8 = -x + 8
\][/tex]
2. Simplify the second polynomial:
[tex]\[
4 + 2x - 7 = 2x + (4 - 7) = 2x - 3
\][/tex]
So, we need to find the product of the simplified polynomials:
[tex]\[
(-x + 8)(2x - 3)
\][/tex]
Next, we distribute each term in the first polynomial to each term in the second polynomial:
1. Multiply [tex]\(-x\)[/tex] by each term in [tex]\(2x - 3\)[/tex]:
[tex]\[
-x \cdot 2x = -2x^2
\][/tex]
[tex]\[
-x \cdot (-3) = 3x
\][/tex]
2. Multiply [tex]\(8\)[/tex] by each term in [tex]\(2x - 3\)[/tex]:
[tex]\[
8 \cdot 2x = 16x
\][/tex]
[tex]\[
8 \cdot (-3) = -24
\][/tex]
Now, combine these results:
[tex]\[
-2x^2 + 3x + 16x - 24
\][/tex]
Combine like terms:
[tex]\[
-2x^2 + 19x - 24
\][/tex]
So, the product of the polynomials [tex]\((5x + 8 - 6x)(4 + 2x - 7)\)[/tex] is:
[tex]\[
-2x^2 + 19x - 24
\][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{-2x^2 + 19x - 24} \][/tex]
So the correct choice is:
A. [tex]\(-2x^2 + 19x - 24\)[/tex]
