(x-6)-find-zeros.jpeg "(x^2+2x-8)(x-6) Find Zeros")
Finding the Zeros of (x^2 + 2x - 8)(x - 6)
To find the zeros of the expression (x^2 + 2x - 8)(x - 6), we need to find the values of x that make the entire expression equal to zero. This can be done by setting each factor equal to zero and solving for x.
Step 1: Factor the quadratic
The quadratic expression (x^2 + 2x - 8) can be factored as (x + 4)(x - 2).
Step 2: Set each factor to zero
We now have the following factors:
- (x + 4)
- (x - 2)
- (x - 6)
Setting each factor equal to zero gives us:
- x + 4 = 0
- x - 2 = 0
- x - 6 = 0
Step 3: Solve for x
Solving for x in each equation gives us:
- x = -4
- x = 2
- x = 6
Therefore, the zeros of the expression (x^2 + 2x - 8)(x - 6) are -4, 2, and 6.
Conclusion:
By factoring the expression and setting each factor to zero, we were able to find the zeros of the expression. These zeros represent the values of x where the expression equals zero. This process is essential for understanding the behavior of polynomial functions and for solving equations involving polynomials.