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Using the Remainder Theorem, Factorise the Expression 3x3 + 10x2 + X – 6. Hence, Solve the Equation 3x3 + 10x2 + X – 6 = 0. Hence, Solve the Equation 3x3 + 10x2 + X – 6=0 - ICSE Class 10 - Mathematics

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Question

Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0. 

Solution

`"Left f "(x)=3x^3+10x^2+x-6` 

`for x =-1,` 

`f(x)=f(-1)=3(-1)^3+10(-1)^2+(-1)-6=-3+10-1-6=0 `

`"Hence,(x+1) is a  factor of f(x)" .` 

 

∴ `3x^3+10x^2+x-6=(x+1)(3x^2+7x-6)` 

                             =`(x+1)(3x^2+9x-2x-6) `

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

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

`now, 3x^3+10x^2+x-6=0` 

`(x+1)(x+3)(3x-2)=0` 

`x=-1, -3, 2/3` 

  Is there an error in this question or solution?
Solution Using the Remainder Theorem, Factorise the Expression 3x3 + 10x2 + X – 6. Hence, Solve the Equation 3x3 + 10x2 + X – 6 = 0. Hence, Solve the Equation 3x3 + 10x2 + X – 6=0 Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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