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ICSE Class 10 Answered

hoow wto use remainder theorem to factoriseee  
Asked by rajatpullinacd | 15 May, 2019, 04:35: PM
Expert Answer
We can't use remainder theorem to find the the factors it is used to find the remainder only.
 
 
Example:

Remainder Therorem:
 
If  x3 + 3x2 -  x + 5 is divided by x + 3, find the remainder.

Let p(x) =x3 + 3x2 -  x + 5
 
By using remainder theorem,
 
x + 3 = 0 → x = -3
→ p(-3) =(-3)3 + 3(-3)2 -  (-3) + 5
            = -27 + 27 + 3 + 5
            = 8
→ Remainder = 8

Factor theorem: It is used to find the factors of the given polynomial
 
Let p(x) =2x3 - 13x2 + 26x - 15
 
Put x = 1 in p(x), we get
 
p(1) =2(1)3 - 13(1)2 + 26(1) - 15
       = 2 - 13 + 26 - 15
       = 0
→ (x - 1) is a factor of p(x)
 
Divide p(x) by (x - 1), we get the quotient (2x2 - 11x + 15).
 
→2x3 - 13x2 + 26x - 15 = (x - 1)(2x2 - 11x + 15)
                                   = (x - 1)(x - 3)(2x - 5)
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