Question

When simplifying 4x^3-10x^2+6x/2x^3+x^2-3x, what are the term(s) that can be cancelled

Answer 1

x can be cancelled

Explanation:

we are given

`(4x^3-10x^2+6x)/(2x^3+x^2-3x)`

Firstly, we will factor numerator and denominator

and then we can factor it

`4x^3-10x^2+6x=2x(2x^2-5x+3)`

`4x^3-10x^2+6x=2x(2x+1)(x-3)`

now, we can factor denominator

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

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

now, we can replace it

`(4x^3-10x^2+6x)/(2x^3+x^2-3x)=(2x(2x+1)(x-3))/(x(x-1)(2x+3))`

we can see that

both terms are having x common

so, x can be cancelled

So,

x can be cancelled