Final answer:
To find the product (ab)(x) of the functions a(x)=-4x-6 and b(x)=2x+5, multiply the two expressions to get -8x^2 - 32x - 30, which is the polynomial in simplest form.
Step-by-step explanation:
To find the product of two functions, in this case (ab)(x) where a(x) = -4x - 6 and b(x) = 2x + 5, you simply multiply the two function expressions together. So, let's multiply a(x) by b(x):
a(x) * b(x) = (-4x - 6)(2x + 5).
Now, distribute each term in the first polynomial by each term in the second polynomial:
-4x * 2x = -8x^2
-4x * 5 = -20x
-6 * 2x = -12x
-6 * 5 = -30
Combine like terms:
-8x^2 - 20x - 12x - 30 = -8x^2 - 32x - 30.
There you have the product of the two functions in simplest polynomial form.