To express the given expression [tex]\((x - 8)(2x + 5)\)[/tex] as a trinomial, we need to use the distributive property (also known as the FOIL method for binomials). Here's a step-by-step breakdown:
1. First Term: Multiply the first terms in each binomial.
[tex]\[
x \cdot 2x = 2x^2
\][/tex]
2. Outer Term: Multiply the outer terms in the binomial.
[tex]\[
x \cdot 5 = 5x
\][/tex]
3. Inner Term: Multiply the inner terms in the binomial.
[tex]\[
-8 \cdot 2x = -16x
\][/tex]
4. Last Term: Multiply the last terms in each binomial.
[tex]\[
-8 \cdot 5 = -40
\][/tex]
Next, we combine all these results together:
[tex]\[
2x^2 + 5x - 16x - 40
\][/tex]
Finally, combine the like terms (the [tex]\(x\)[/tex] terms in this case):
[tex]\[
2x^2 + (5x - 16x) - 40 = 2x^2 - 11x - 40
\][/tex]
So, the trinomial expression for [tex]\((x - 8)(2x + 5)\)[/tex] is:
[tex]\[
2x^2 - 11x - 40
\][/tex]
