F (x) = (x - 6) ^2 (x + 2) ^2

Determine the total number of roots of each polynomial function using the factored form

x = 6 or x = - 2

Step-by-step explanation:

Solve for x:

(x - 6) ^2 (x + 2) ^2 = 0

Split into two equations:

(x - 6) ^2 = 0 or (x + 2) ^2 = 0

Take the square root of both sides:

x - 6 = 0 or (x + 2) ^2 = 0

Add 6 to both sides:

x = 6 or (x + 2) ^2 = 0

Take the square root of both sides:

x = 6 or x + 2 = 0

Subtract 2 from both sides:

Answer: x = 6 or x = - 2