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Using the Remainder Theorem, Factorise Each of the Following Completely. 3x3 + 2x2 – 23x – 30 - Mathematics

Using the Remainder Theorem, factorise each of the following completely. 

3x3 + 2x2 – 23x – 30

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Solution

`f(x)=3x^3+2x^2-23x-30` 

for x=-2, 

`f(x)=f(-2)=3(-2)^3+2(2)^2-23(-2)-30` 

=`-24+8+46-30=-54+54=0` 

Hence, (x+2)is a factor of  f(x). 

  

∴ `3x^3+2x^2-23x-30=(x+2)(3x^2+4x-15)` 

                                   =`(x+2)(3x^2+5x-9x-15)` 

                                  = `(x+2) [x(3x+5)-3(3x+5)]` 

                                 =  `(x-2) (3x+5)(x-3)` 

Concept: Factor Theorem
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