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Using the Factor Theorem, Show That: (X – 2) is a Factor of X3 – 2x2 – 9x + 18. Hence, Factorise the Expression X3 – 2x2 – 9x + 18 Completely. - ICSE Class 10 - Mathematics

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Question

Using the Factor Theorem, show that:

 (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.

Solution

Let f(x)=`x^3-2x^2-9x+18`  

x-2=0 ⇒ x=2 

∴ Remainder =f(2) 

= `(2)^3-2(2)^2-9(2)+18`    

=`8-8-18+18` 

=`0` 

Hence, (x-2) is a factor of f (x) 

Now, we have: 

 

 ∴ `x^3-2x^2-9x+18=(x-2)(x^2-9)=(x-2)(x+3)(x-3) `  

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Solution Using the Factor Theorem, Show That: (X – 2) is a Factor of X3 – 2x2 – 9x + 18. Hence, Factorise the Expression X3 – 2x2 – 9x + 18 Completely. Concept: Factor Theorem.
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