Question

factorize 3x^3 - x^2 + x​

Answer 1

Your Answer:

Given :

$p(x) = 3 {x}^{3} - {x}^{2} + x$

Required to solve :

1. Factorisation of P(x)

Solution :

In this question we were asked to factorise an cubic expression generally cubic expression cannot be solved by splitting the middle terms but in some cases it can be solved .So, To factorise this equation we need to use the factor theorem.

so, I think you may be wondering what a factor theorem is .

let me explain you about factor theorem simply it is very useful..

Factor theorem :

Actually a factor theorem states that for an given expression that is p(x) if (x-a) when substituted in p(x) will gives under an remainder zero.

Simply , this is nothing but (x-a) is a factor of p(x) this means when we substitute a in place of x we get the remainder zero.

This is factor theorem.

Here we have follow the method of hit trial and error method to find the factor of p(x) or given cubic Expression.

You will learn about this method in detail in your higher studies.

Now,

simple solution :

Here I am giving the easiest and shortcut method to solve the above equation or Expression.

$3 {x}^{3} - {x}^{2} + x \\ 3x( {x}^{2} - x + 1) \\ 3x( {x}^{2} + 1x - 1x + 1) \\ 3x( x(x + 1) - 1(x + 1)) \\ 3x((x + 1)(x - 1))$

Therefore ,

This is your required answer...