Final answer:
To find the resulting polynomial of f(x)*g(x), we need to multiply the two polynomials term by term. The resulting polynomial is -10x^3 - 46x^2 - 74x - 30.
Step-by-step explanation:
To find the resulting polynomial of f(x)*g(x), we first need to multiply the two polynomials term by term. Let's multiply each term of f(x) = 10x + 6 with each term of g(x) = -x^2 - 4x - 5:
f(x)*g(x) = (10x + 6) * (-x^2 - 4x - 5)
Using distributive property, we multiply each term of f(x) by each term of g(x):
f(x)*g(x) = (10x * -x^2) + (10x * -4x) + (10x * -5) + (6 * -x^2) + (6 * -4x) + (6 * -5)
Simplifying the expression, we get:
f(x)*g(x) = -10x^3 - 40x^2 - 50x - 6x^2 - 24x - 30
Combining like terms, we have the resulting polynomial:
f(x)*g(x) = -10x^3 - 46x^2 - 74x - 30