THANK YOU SO MUCH, I KNOW THIS IS A LOT OF WORK!! (1) Factor the polynomial. Show your work. -3x^4 - 9x^3 + 15x^2 (2) Use the grouping method to factor the polynomial below completely. Show your work. 10x³ - 35x² + 6x - 21 (3) Factor the following trinomial. x² - 15x + 56 (the rest of the problem and the steps I have to follow are below) Step 1: The trinomial factors are x² + bx + c = (x+p)(x+q), where p + q = b and p · q = c. Fill in the following table with all of the possible values of p and q, using the fact that their product is the constant term, c = 56. P ║ Q ║ P+Q 1 ║ 56 ║ 57 -1 ║ -56 ║ -57 2 ║ 28 ║ 30 -2 ║ -28 ║ -30 ? ║ ? ║ ? ? ║ ? ║ ? ? ║ ? ║ ? ? ║ ? ║ ? (I tried making columns so its easier to see the table, just fill in the last four rows) Step 2: Which factors for P and Q add to equal the coefficient of the x-term (-15) in the trinomial? Step 3: Using the factors from Step 2, write the trinomial x² - 15x + 56 in factored form. (4) Factor the trinomial completely. Show your work. 3x² - 18x + 24 (5) Factor each trinomial completely. Show your work. (a) 2x² + 17x + 21 (b) 3x² - 17x + 10 (6) Factor each trinomial completely. Show your work. (a) x² - 81 (b) 4x² - 25b² (7) Factor each polynomial. Show your work. (a) x² + 14x + 49 (b) x² - 16x + 64 (8) Use factoring to find the zeros of f(x) = x² + 3x - 18. Steps below. (a) First factor the polynomial x² + 3x - 18. (b) Use the factors from Part A to find the zeros of f(x) = x² + 3x - 18. (9) Use the graph of each polynomial function to dine the factored form of the related polynomial. Assume the polynomial has no constant factor. (A) What are the zeros of the function? _ , _ What is the factorization of the polynomial? _ (graph titled, "Graph #1" attached below) (B) What are the zeros of this function? _ , _ . What is the factorization of the polynomial? _ . (graph titled, "Graph #2" attached below) (10) A paper airplane is thrown off a 64-foot bridge into the water below. Its height, in feet, is represented by f(x) = -16(x² - 3x - 4), where x is the number of seconds since the airplane was thrown. The height of the airplane is 0 feet when it hits the water. (graph titled, "Graph #3" attached below) (A) Factor the polynomial expression -16(x² - 3x - 4). Show your work. (B) Use the factorization from Part A to identify the zeros of the function. Show your work. (C) What do the zeros mean in terms of the situation? (D) Do both zeros have a real-world meaning? (E) How long does it take the airplane to hit the water? THANKS AGAIN