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6 - Chapter 2 Review Date: 1 . i. Use the remainder theorem to determine the remainder for each division. ii. Perform cach division. Express the result in quotient form. Identify all restrictions on the variable. (a) 13 + 4x2 - 3 divided r - 2 (b) 323 - 5r2 + 2r - 6 divided by r - 5 (c) 274 - 313 - 4x2 + 5x - 15 divided by 2r + 1 2. Determine the value of & such that when f(r) = 315 - 423 + ke? - 1 is divided by + + 2, the remainder is -5. by r + 2 and 2 - 37 3. For what value of m will the polynomial P(2) = 2.23 + ma? - 4r + 1 have the same remainder when it is divided 1. When f(x) = 4x3 + mx2 - nr + 8 is divided by x - 3 the remainder is 155. When f(r) is divided by r + 5 the remainder is -397. Determine the values for m and n. 5. List the values that could be zeros of each polynomial. Then, factor the polynomial. (a) 13+ 12 - 10r + 8 (b) 2x3 + 723 + 71 + 2 (c) 314 + 23 - 1412 - 4r + 8 6. Solve. (a) 23 - 312 - 9r + 27 = 0 (b) 4x3 + 4x2 - 25x - 25 = 0 (c) 923 + 1813 - 4x - 8 =0 7. Determine the value of b such that a + 4 is a factor of 213 - 412 + br - 8 8. Determine the value of k such that 3x - 2 is a factor of a3 + kr? - 5x + 3. 9. (a) Determine an equation for the family of cubic functions with zeros - }, 2, and 6 (b) Write equations for two functions that belong to the family in part (a). (c) Determine an equation for the member whose graph passes through the point (-1, 42). 10. (a) Determine an equation, in simplified form, for the family of cubic functions with zeros -3 and 1 + v (b) Determine an equation for the member of the family whose y-intercept is -10. 11. Solve each inequality. (a) (4r + 5)(x + 2) 20 (b) (3x - 1)(2x + 5)(3 -x) 50 (c) (412 -9)(x2 + 61 + 9) >0 (d) -23 -x2 + 9r +9>0 (e) 24 - 423 -21x2 + 100x - 100 5 0