You are given f(x) = x^4 - 3x^3 - kx - 5. When f(x) is divided by x + 2, the remainder is 51.a. Determine the value of k using the remainder theorem. b. Using your value of k from part a, determine the remainder when f(x) is divided by x - 3. 13. Solve the following equations algebraically using long or synthetic division. Then use technology to sketch the graph and confirm your answer. Make sure to label x-ints, y-ints, and intersections.a. 2x^3+3x^2-11x-6=0b. x^3-14x - 10 = 14 - x^2

12. You are given f(x) :x4 3x3 kx 5. When flx) is divided be+ 2, the remainder is 51. a. Determine the value of k using the remainder theorem. (2) b. Using your value of k from part 3, determine the remainder when f(x) is divided by x 3. ll) 13. Solve the following equations algebraically using long or synthetic division. Then use technology to sketch the graph and confirm your answer. Make sure to label X-ints, y-ints, and intersections. (6) a. 2x3+3x211x6=0 b. )(314x10=14x2