Determine all zeros for the function f(x)=(x2+2x−8)(x−6).

To find the zeros of the function f(x)=(x^2+2x-8)(x-6), we need to set the function equal to zero and solve for x.

Step 1: Set the function equal to zero 0 = (x^2+2x-8)(x-6)

Step 2: Set each factor equal to zero and solve for x x^2+2x-8 = 0 and x-6 = 0

Solving x^2+2x-8 = 0: This is a quadratic equation in the form ax^2+bx+c=0. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, the equation factors easily:

(x+4)(x-2) = 0

Setting each factor equal to zero gives the solutions x=-4 and x=2.

Solving x-6 = 0: This is a linear equation, which we can solve by adding 6 to both sides to get x=6.

So, the zeros of the function f(x)=(x^2+2x-8)(x-6) are x=-4, x=2, and x=6.