Factor Theorem Exercise 1. If (? + 8) is a factor of f(?) , then what is the value of f(-8) ? 2. If f(?) = 2 3 +2? 2 -5? -6 is equal to 0 when ? = -1 or 2 or - 3, what are the factors of f(?)? 3. For each of the following, determine whether the binomial is a factor of f(?) using the Factor Theorem. a) (? + 2); f(?) = ? 2+8?+6 b) (? - 2): f(?) = ? 3 -3? 2 -42+12 c) (? + 1); f(?) = ? 3-5? 2-42+3 d) (2? - 1); f(?) = 42 3 -67 2 +8?-3 4. Factor completely. Use the Factor Theorem. a) ?3 -4?+3 b) ?3 + 2? 2 -?-2 c) ?3 + 19? 2 - 19? - 1 d) ?3 +2? 2 +5?+4 e) ?3 -?2 -?-2 f) ?3 - 9? 2 + 22? - 8 g) ?4 - 8? 3+ 3? 2 + 40? - 12 h) ?4 -6? 3 - 15? 2 -6?-16 5. Factor completely. Use the Extended Factor Theorem. a) 2?3 +?2 +?-1 b) 5?3 +3? 2 - 12?+4 c) 5?4 + ? 3 - 22? 2-4? +8 d) 18? 3 - 15? 2 -?+2 ANSWERS -81