Let f(x) = x^3 + 2x^2 + 3x + 1 and g(x) = 4x - 5.
Find f(x) x g(x).
To find f(x) x g(x), we need to multiply the two functions:
f(x) x g(x) = (x^3 + 2x^2 + 3x + 1) x (4x - 5)
To multiply these two polynomials, we can use the distributive property:
f(x) x g(x) = x^3 x (4x - 5) + 2x^2 x (4x - 5) + 3x x (4x - 5) + 1 x (4x - 5)
Now let's multiply each term individually:
f(x) x g(x) = 4x^4 - 5x^3 + 8x^3 - 10x^2 + 12x^2 - 15x + 4x - 5
Combining like terms:
f(x) x g(x) = 4x^4 + 3x^3 + 2x^2 - 11x - 5
Therefore, f(x) x g(x) = 4x^4 + 3x^3 + 2x^2 - 11x - 5.