Let f(x)= 4x(x+3)^2 - (x+3)^3 and find the values of x that correspond to f(x)=0.
Factor it first
(x+3)(x+3) [4x -(x+3)] = 0
(x+3)(x+3)[3x-3] = 0
x = -3
x = -3
x = +1
Thank you!
To find the values of x that correspond to f(x) = 0, we need to solve the equation 4x(x+3)^2 - (x+3)^3 = 0.
Step 1: Factor out the common factor (x+3)^2.
f(x) = (x+3)^2(4x - (x+3))
Step 2: Set each factor equal to zero and solve for x.
(x+3)^2 = 0 or (4x - (x+3)) = 0
For the first factor, (x+3)^2 = 0, we can take the square root of both sides to get:
x+3 = 0
x = -3
For the second factor, we simplify:
4x - (x+3) = 0
3x - 3 = 0
3x = 3
x = 1
Therefore, the values of x that correspond to f(x) = 0 are x = -3 and x = 1.