What are the solutions to the equation y = (x-4)(x+5)(x-1)?
To find the solutions to the equation y = (x-4)(x+5)(x-1), we need to find the values of x where y equals zero. In other words, we are looking for the x-intercepts or the values that make y equal to zero.
To solve this equation, we will set y equal to zero and solve for x:
0 = (x-4)(x+5)(x-1)
Since a product of factors is equal to zero if and only if at least one of the factors is equal to zero, we can set each factor equal to zero and solve for x.
Setting the first factor equal to zero:
x - 4 = 0
x = 4
Setting the second factor equal to zero:
x + 5 = 0
x = -5
Setting the third factor equal to zero:
x -1 = 0
x = 1
Therefore, the solutions to the equation y = (x-4)(x+5)(x-1) are x = 4, x = -5, and x = 1. These are the values of x where the equation y equals zero or the x-intercepts of the graph of the equation.
To find the solutions to the equation y = (x-4)(x+5)(x-1), we need to set y equal to zero and solve for x.
Step 1: Set y equal to zero
0 = (x-4)(x+5)(x-1)
Step 2: Use the zero-product property
The zero-product property states that if a product of factors equals zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x.
x-4 = 0 or x+5 = 0 or x-1 = 0
Step 3: Solve for x in each equation
For x-4 = 0:
x = 4
For x+5 = 0:
x = -5
For x-1 = 0:
x = 1
Therefore, the solutions to the equation are x = 4, x = -5, and x = 1.