Remainder And Factor Theorems

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Remainder And Factor Theorems
MyElimu Offline
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Not Solved Post Icon Remainder And Factor Theorems

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 1. Remainder Theorem

If a polynomial f(x) is divided by x - a, then the remainder, R = f(a).

2. Factor Theorem
If 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 3Example Questions
[Image: Screen%20shot%202011-03-17%20at%20PM%2004.39.09.png]

Note: How to divide f(x) by (x + 1)
[Image: Screen%20shot%202011-03-17%20at%20PM%2004.44.55.png]
Note: How to factorize 4x2 -12x +9
[Image: Screen%20shot%202011-03-17%20at%20PM%2004.47.53.png]
 [Image: Screen%20shot%202011-03-17%20at%20PM%2004.56.42.png]
[Image: Screen%20shot%202011-03-17%20at%20PM%2004.57.02.png]

Questions

[Image: Screen%20shot%202011-03-17%20at%20PM%2005.12.50.png]

Answers1a. -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

 
03-11-2014 11:35 AM
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