Question

Given f(x) = 5x^2 and g(x) = x^3 + 2x^2 - 5x, what is f(x) · g(x)?

a) 5x^5 - 5x^3 - 10x^2
b) 5x^5 + 5x^3 - 10x^2
c) 5x^5 + 10x^4 - 10x^3
d) 5x^5 + 10x^3 - 5x^2

Answer 1

To find the product of f(x) and g(x), each term of f(x) must be multiplied by each term of g(x). The correct product is 5x⁵ + 10x⁴ - 25x³.

Step-by-step explanation:

When multiplying two functions, f(x) and g(x), we simply multiply each term of f(x) by each term of g(x). In this case:

f(x) = 5x²
g(x) = x³ + 2x² - 5x

Then the product f(x) · g(x) is found by multiplying each term from f(x) by each term of g(x):

1. Multiply 5x² by x³: 5x⁵
2. Multiply 5x² by 2x²: 10x⁴
3. Multiply 5x² by -5x: -25x³

After multiplying, we combine the like terms:

• There are no like terms with 5x⁵, so it remains as is.
• 10x⁴ is the only term with x to the fourth power.
• There are no like terms with -25x³, so it remains as is.

Therefore, the product f(x) · g(x) is 5x⁵ + 10x⁴ - 25x³, which corresponds to choice c) 5x⁵ + 10x⁴ - 25x³.