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(3x + 2) is a Factor of 3x3 + 2x2 – 3x – 2. Hence, Factorise the Expression 3x3 + 2x2 – 3x – 2 Completely. - ICSE Class 10 - Mathematics

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Question

 (3x + 2) is a factor of 3x3 + 2x2 – 3x – 2. Hence, factorise the expression 3x3 + 2x2 – 3x – 2 completely.

Solution

Let f(x)=`3x^3+2x^2-3x-2` 

`3x+2=0`  ⇒ `x=(-2)/3` 

∴ Remainder = f `((-2)/3)` 

     =`3((-2)/3)^3+2((-2)/3)^2-3((-2)/3)-2` 

    = `(-8)/9+8/9+2-2` 

    = 0 

Hence,(3x+2) is a factor of f (x) 

Now, we have: 

  

∴ `3x^3+2x^2-3x-2=(3x+2)(x^2-1)=(3x+2)(x+1)(x-1)` 

  Is there an error in this question or solution?

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Solution (3x + 2) is a Factor of 3x3 + 2x2 – 3x – 2. Hence, Factorise the Expression 3x3 + 2x2 – 3x – 2 Completely. Concept: Factor Theorem.
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