Question

SOLVE BY FACTORING...THANK YOU

2X^3 - 5X^2 - 3X=0

Answer 1

Take out x as the common factor:
x(2x^2-5x-3)=0;
From here, you can just factorise normally or complete the square.
x(2x^2+x-6x-3)=0;
x(x(2x+1)-3(2x+1))=0;
x(2x+1)(x-3)=0;
x=-1/2,0,3

Answer 2

2 x³ - 5 x² - 3 x = 0

x ( 2 x² - 5 x - 3 ) = 0

Factor of 2 x² - 5 x - 3:

2 x² - 5 x - 3 = ( 2 x² + x ) - 6 x - 3 = x ( 2 x + 1 ) - ( 6 x + 3 ) =

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

( 2 x + 1 ) ∙ x - ( 2 x + 1 ) ∙ 3 = ( 2 x + 1 ) ( x - 3 )


2 x³ - 5 x² - 3 x = x ( 2 x + 1 ) ( x - 3 )


Using the Zero Factor Principle: If a b = 0 then a = 0 or b = 0 or both a = 0 and b = 0

In this case x = 0 and ( 2 x + 1 ) ( x - 3 ) = 0

So one of solution is x = 0

Now solve 2 x + 1 = 0

2 x = - 1

x = - 1 / 2

Solve x - 3 = 0

x = 3

The solutions are:

x = - 1 / 2 , x = 0 and x = 3