#### Question

Using the Remainder Theorem, factorise the expression 3x^{3} + 10x^{2} + x – 6. Hence, solve the equation 3x^{3} + 10x^{2} + 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.