MHF4U /2.2 - The Remainder / Factor Theorem Date: Perform each division. Express the result in quotient form. Identify any restrictions on the variable. (a) x3 + 2x2 - 5x + 2 divided by x + 2 (b) 4x3 + 3x - 4 divided by 2x + 1 (c) -9x4 + 6x3 + 6x - 5 divided by 3x - 2 Use the remainder theorem to determine the remainder for each division. (a) 23 - 3x2 + 5x - 2 divided by x - 4 (b) 3x3 + x2 - 4x + 10 divided by a + 3 (c) x4 + 2x3 - 3x + 2 divided by 2x - 1 When the polynomial mr3 + 5x2 - nx - 1 is divided by x - 1, the remainder is 2. When the same polynomial is divided by x + 3, the remainder is 10. Determine the values of m and n. Determine if x - 2 is a factor of each binomial. (a) 3x3 - x2 +2x (b) x3 +2x2 - 16 (c) 2x3 - 3x2 + 1 - 6 List all of the possible values that could be zeros for each polynomial and then factor each polynomial. (a) x3 +5x2 -x -5 (b) 23 - 7x+6 (c) x3 - 3x2 - 4x + 12 List all of the possible values that could be zeros for each polynomial and then factor each polynomial. (a) 2x3 + 11x2 + 2x - 15 (b) 3x3 +8x2 +3.x -2 (c) 5x3 - 17x2 + 16x - 4 7. Determine a polynomial function P(x) that satisfies the following set of conditions: P(2) = P (3) = P(-5) =0 and P(9) = -100