# Equations – Factorization of a polynomial equation – Exercise 5625

## Exercise

Factor the polynomial equation

$$10x^4-15x^3-4x^2+6x=0$$

$$x(2x-3)(5x^2-2)$$

## Solution

$$10x^4-15x^3-4x^2+6x=$$

We extract a common factor

$$=x(10x^3-15x^2-4x+6)=$$

Again we extract common factors in the parentheses

$$=x(5x^2(2x-3)-2(2x-3))=$$

Once again we extract a common factor – this time the expression in parentheses:

$$=x(2x-3)(5x^2-2)$$

Share with Friends