Let f(x)=x^3 + 2x^2 +3x +1 and g(x)=4x-5
Find f(x)*g(x)
To find f(x)*g(x), we need to multiply the two polynomials together:
f(x) * g(x) = (x^3 + 2x^2 + 3x + 1) * (4x - 5)
To do this, we will use the distributive property and multiply each term of f(x) by g(x):
f(x) * g(x) = (x^3 + 2x^2 + 3x + 1) * 4x + (x^3 + 2x^2 + 3x + 1) * (-5)
Multiplying the first term:
(x^3 + 2x^2 + 3x + 1) * 4x = 4x^4 + 8x^3 + 12x^2 + 4x
Multiplying the second term:
(x^3 + 2x^2 + 3x + 1) * -5 = -5x^3 - 10x^2 - 15x - 5
Now, we add the two terms together:
f(x) * g(x) = (4x^4 + 8x^3 + 12x^2 + 4x) + (-5x^3 - 10x^2 - 15x - 5)
Simplifying the equation further:
f(x) * g(x) = 4x^4 + (8 - 5) x^3 + (12 - 10) x^2 + (4 - 15) x + (-5)
f(x) * g(x) = 4x^4 + 3x^3 + 2x^2 - 11x - 5
Therefore, f(x)*g(x) = 4x^4 + 3x^3 + 2x^2 - 11x - 5.