Notes1. Remainder TheoremIf a polynomial f(x) is divided by x - a, then the remainder, R = f(a).
2. Factor TheoremIf f(a) = 0, then (x - a) is a factor of f(x)
3. Solutions of EquationsTo solve the equation f(x) = 0, first factorize f(x) by the Factor Theorem
Eg . solve x3 - 2x2 - 5x + 6 = 0 Let f(x) = x3 - 2x2 - 5x + 6 Find a factor by trial and error eg, found that (x - 1) is a factor
Divide f(x) by (x - 1) and we get
f(x) = (x - 1)(x2 - x - 6)
Factorize x2 - x - 6
---> f(x) = (x - 1)(x + 2)(x - 3) so, (x - 1)(x + 2)(x - 3) = 0 so x = 1, -2, or 3
Example Questions Note: How to divide f(x) by (x + 1) Note: How to factorize 4x2 -12x +9
QuestionsAnswers1a. -2, 3, 5 1b. 1, -2, -1/2 1c. 1/2, -1/2, 2/3 2. 2 3a. a = 3, b = 8 3b. (2x - 1)(x - 1) 4. -2 5. c = 0 , 3, -3
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