Factor: x2 + 25 Use the Binomial Theorem and Pascal's triangle to expand (x + 2)4. Given the function. f(x) = x3 5x2 + 9x 45, determine the number of roots and identify them. Explain the closure property as it relates to rational expressions. Give an example and simplify it to prove closure. 4 _1 George tells you that when variables are in the denominator, the equation 5 X 2 becomes unsolvable. George explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to George how the equation is still solvable and explain your reasoning. (10 points) f(x) = (x- 1)(x+2)(x+4) When looking at the rational function (x + 1)(x-2)(x-4) Bella and Edward have two different thoughts. Bella says that the function is defined at x = -1, x = 2, and x = 4. Edward says that the function is undefined at those x values. Who is correct? Justify your reasoning. (10 points)Jean and Mark are going to fill a pool with 2 different sized hoses. Jean can fill the pool in 8 hours, while Mark can complete it in 12 hours. Their supervisor thinks that the job will take 10 hours to complete if they work together. Explain each step in solving this equation, and determine if the supervisor is correct or not. (10 points)Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jimmy to complete this job on his own. (10 points)