Answer :
We are given the functions
[tex]$$
f(x) = -5x \quad \text{and} \quad g(x) = 8x^2 - 5x - 9.
$$[/tex]
To find the product [tex]$(f \cdot g)(x)$[/tex], we multiply [tex]$f(x)$[/tex] by [tex]$g(x)$[/tex]:
[tex]$$
(f \cdot g)(x) = f(x) \cdot g(x) = (-5x)(8x^2 - 5x - 9).
$$[/tex]
Now, distribute [tex]$-5x$[/tex] to each term of [tex]$g(x)$[/tex]:
1. Multiply [tex]$-5x$[/tex] by [tex]$8x^2$[/tex]:
[tex]$$
-5x \cdot 8x^2 = -40x^3.
$$[/tex]
2. Multiply [tex]$-5x$[/tex] by [tex]$-5x$[/tex]:
[tex]$$
-5x \cdot (-5x) = 25x^2.
$$[/tex]
3. Multiply [tex]$-5x$[/tex] by [tex]$-9$[/tex]:
[tex]$$
-5x \cdot (-9) = 45x.
$$[/tex]
Now, combine the results:
[tex]$$
(f \cdot g)(x) = -40x^3 + 25x^2 + 45x.
$$[/tex]
Thus, the final answer is:
[tex]$$
\boxed{-40x^3 + 25x^2 + 45x}.
$$[/tex]
[tex]$$
f(x) = -5x \quad \text{and} \quad g(x) = 8x^2 - 5x - 9.
$$[/tex]
To find the product [tex]$(f \cdot g)(x)$[/tex], we multiply [tex]$f(x)$[/tex] by [tex]$g(x)$[/tex]:
[tex]$$
(f \cdot g)(x) = f(x) \cdot g(x) = (-5x)(8x^2 - 5x - 9).
$$[/tex]
Now, distribute [tex]$-5x$[/tex] to each term of [tex]$g(x)$[/tex]:
1. Multiply [tex]$-5x$[/tex] by [tex]$8x^2$[/tex]:
[tex]$$
-5x \cdot 8x^2 = -40x^3.
$$[/tex]
2. Multiply [tex]$-5x$[/tex] by [tex]$-5x$[/tex]:
[tex]$$
-5x \cdot (-5x) = 25x^2.
$$[/tex]
3. Multiply [tex]$-5x$[/tex] by [tex]$-9$[/tex]:
[tex]$$
-5x \cdot (-9) = 45x.
$$[/tex]
Now, combine the results:
[tex]$$
(f \cdot g)(x) = -40x^3 + 25x^2 + 45x.
$$[/tex]
Thus, the final answer is:
[tex]$$
\boxed{-40x^3 + 25x^2 + 45x}.
$$[/tex]
