5. Determine the equation of the quartic function with x-intercepts of 2, 3, -1 and whose graph touches the x-axis at (3,0). The graph also passes through (4,-10) . Leave your answer in factored form. (3 marks) 6. Determine the remainder when P(x) = x* + 2x/ +5x+4 is divided by each binomial. Use the remainder theorem. a) x-2 (2 marks) b) x+3 (2 marks) Mathematics 30-1: Module 3 15 7. When the polynomial 2x + bx -5 is divided by x-3, the remainder is 7. a) Determine the value of b. (2 marks) E b) What is the remainder when the polynomial is divided by x-2? (1 mark) 8. Determine the value of k if x+4 is a factor of P(x) = 3x* +1 1x -6x +k. (2 marks)Mathematics 30-1: Module 3 13 3. The polynomial shown at the beginning of the lesson could be written as P(x) = x* + 3x2 - x - 3. adapted from Stockbyle/Thinkstock Determine if each of the following binomials is a factor of the polynomial P(x) = x3 + 3x2 - x - 3? Explain your answers a. x - 1 (2 marks) b. x + 1 (2 marks) c. x - 3 (2 marks) d. x + 3 (2 marks) E Mathematics 30-1: Module 3 14 4. A cubic function has zeros -3, and 4 (multiplicity of 2). The graph of the function passes through (5,12). Determine the equation of the function in factored form. (2 marks)