Question

Factor.1) x³ - 2x² - 8x = 0

Answer 1

GIVEN:

We are given the following polynomial equation;

`x^3-2x^2-8x=0`

Required;

Factorize the equation.

Step-by-step solution;

We begin by taking out the common factor, and that is x;

`\begin{gathered} x^3-2x^2-8x=0 \\ \\ x(x^2-2x-8)=0 \end{gathered}`

Therefore we have,

`\begin{gathered} Using\text{ }the\text{ }zero\text{ }factor\text{ }principle: \\ \\ x=0,(x^2-2x-8)=0 \end{gathered}`

Next we factorize the expression in parenthesis;

`\begin{gathered} x^2-2x-8=0 \\ \\ Apply\text{ }the\text{ }sum\text{ }product\text{ }rule: \\ \\ -2x=+2x-4x \\ \\ x^2+2x-4x-8=0 \\ \\ (x^2+2x)-(4x+8)=0 \\ \\ x(x+2)-4(x+2)=0 \\ \\ (x-4)(x+2)=0 \end{gathered}`

Therefore the three factors are;

`\begin{gathered} x=0 \\ (x-4)=0 \\ (x+2)=0 \end{gathered}`

ANSWER:

`x(x-4)(x+2)=0`