Final answer:
To find the product (f(x)) * (8(x)), distribute each term in f(x) with each term in 8(x), then combine like terms to obtain the final result, which is 2x^3 + 13x^2 + 19x + 20.
Step-by-step explanation:
Multiplying Polynomials
To find the product of (f(x)) * (8(x)) when f(x) = 2x^2 + 3x + 4 and 8(x) = x + 5, we must use the distributive property, also known as the FOIL method, to multiply these polynomials. First, distribute each term in the first polynomial with each term in the second polynomial:
- (2x^2)(x) = 2x^3
- (2x^2)(5) = 10x^2
- (3x)(x) = 3x^2
- (3x)(5) = 15x
- (4)(x) = 4x
- (4)(5) = 20
Combine like terms:
- 2x^3 + (10x^2 + 3x^2) + (15x + 4x) + 20
- 2x^3 + 13x^2 + 19x + 20
The final answer is 2x^3 + 13x^2 + 19x + 20.