Please help to do the following, Please do it all on paper with the same format and with all the steps so I can understand better.

Thank you.

1) For the function f(x) =-5(x -3)(2x+ 5)(x +4)', state the following properties. (K - 6 marks) a) Degree: b) Leading coefficient: c) Zeros: d) Number of turning points: e) End behaviour:2) Divide (6x3 -1 1x2 +9) : (2x-1). 3) Divide (3x4 - 2x3 + 3x2 -5x -8) + (x- +3x+1). (K - 3 marks) (K - 3 marks)Factor 2x*+ x3-23x2 -46x -24. (A - 4 marks) 4)5) Factor 40x' +135x2. (A - 3 marks)20 6) For the graph of a polynomial function shown on the right, state 15 whether the leading coefficient of the polynomial is positive or 10 negative, and whether its degree is even or odd. (K -2 marks) Sign of leading coefficient: -2 -1 2 3 -5 Degree even or odd: -10 -15 -20J I 7) The graph on the left was obtained by transforming the graph of y = x3 . Determine the equation of the graph. (A 3 marks) 8) Sketch the graph of f{x) = 1" 4x3 20x2 + 48x using the zeros and end behaviour. Be sure to show all calculations. (1' 6 marks} 9) Determine the equation of the degree 6 polynomial shown on the right. You may leave your answer in factored form. (I 3 marks} 300 -3DD -4DD -500 -500 10) The function f{x} = of +59:2 +116x + 30 has a factor ofx 3. Furthermore, whenx) is divided by x + l, the remainder is 96. Determine the values of a and b. (I 3 marks] 11) A student named Polly Nomial claimed that the function f(x) = -3(2x +4)' -1 has local maxima and minima. Is Polly's claim correct? Explain. (C-2 marks)12) Complete the following table. (C -4 marks) Type of Polynomial Minimum Number Maximum Number Minimum Number Maximum Number Function of Zeros of Zeros of Turning Points of Turning Points Cubic Quartic