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Using the Remainder Theorem, Factorise Each of the Following Completely. 2x3 + X2 – 13x + 6 - ICSE Class 10 - Mathematics

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Question

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

 2x3 + x2 – 13x + 6 

Solution

Let f(x) = `2x^3+x^2-13x+6` 

for x=2 

Factors of constant term 6 are ≠1, ≠ 2, ≠ 3, ≠ 6.
Putting x = 2, we have:

`f(x)=f(2) =2(2)^3+(2)^2-13(2)+6=16+4-26+6=0` 

Hence, (x-2) is a factor of f (x) 

  

∴ `2x^3+x^2-13x+6=(x-2)(2x^2+5x-3)`

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

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

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

  Is there an error in this question or solution?

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Solution Using the Remainder Theorem, Factorise Each of the Following Completely. 2x3 + X2 – 13x + 6 Concept: Factor Theorem.
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