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Using the Remainder Theorem, Factorise Each of the Following Completely. 3x3 + 2x2 − 19x + 6 - ICSE Class 10 - Mathematics

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Question

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

3x+ 2x2 − 19x + 6 

Solution

For x=2, the value of the given 

expression `3x^3+2x^2-19x+6` 

= `3(2)^3+2(2)^2-19(2)+6` 

=`24+8-38+6` 

= 0 

⇒ x-2 is a factor of `3x^3+2x^2-19x+6` 

Now let us do long division 

  

Thus we have , 

`3x^3+2x^2-19x+6` =`(x-2)  (3x^2+8x-3) ` 

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

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

                                 = (x-2) (3x-1) (x+3) 

  Is there an error in this question or solution?

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Solution Using the Remainder Theorem, Factorise Each of the Following Completely. 3x3 + 2x2 − 19x + 6 Concept: Remainder Theorem.
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