Find all zeros of each function. List all possible rational zeros first.

x = 2; x = -1 ; x = -4

Step-by-step explanation:

The zeroes of the function are the values of x where f(x) is zero. We can find these values by setting the function to zero and solving for those values of x.

                     Let   x³ + 3x² - 6x - 8 = 0

Since the function cubic and has a term without x we first have to find a factor through trial and error to make factorization easy.

Since when x = 2; f(x) = (2³) + 3(2)² - 6(2) - 8 = 0

            then ⇒ x - 2 = 0 is a factor of f(x) & x = 2 is a zero of the function

Now we can use the long division to factor f(x)

      [see picture below for this step]

Now, since f(x) = (x - 2) (x² + 5x + 4)

  then (x - 2) (x² + 5x + 4) = 0

⇒ x² + 5x + 4 = 0  [a]       or x -2 = 0

Now let's factor [a]

           x² + 5x + 4 = 0

           x² + 4x + x + 4 = 0

           (x + 1) (x + 4) = 0

⇒ x = 2 x = -1 ; x = -4 are the zeroes of the function

27 + 13x + 15 = (x + 5)( =

step-by-step explanation:

27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( =