Question

How do I factor the following equation in the link? It has been factored, but I need to know the steps.

Answer 1

Given

$2x^2-x-3=0$

How to factor

Solution

Step 1

Multiply the first and last costant

$-3\times2x^2=-6x^2$

Step 2

Write out all the pair factors of -6x^2

$\begin{gathered} -6x^2=-6x\text{ and x} \\ -6x^2=-x\text{ and 6x} \\ -6x^2=\text{ -3x and 2x} \\ -6x^2=\text{ -2x and 3x} \end{gathered}$

Step 3

Check for the pair, such that when you add you will get -x

$\begin{gathered} it\text{ is } \\ -3x+2x=-x \\ \therefore-3x,\text{ 2x} \end{gathered}$

Step 4

Replace -x with -3x+2x in the equation

$2x^2-3x+2x-3=0$

Step 5

Put them into brackets Since + is at the center no stress.

$(2x^2-3x)+(2x-3)=0$

Step 6

Factor out what is common in the bracket

$x(2x^{}-3)+1(2x-3)=0$

Step 7

What is in the bracket are the same, pick one

$\therefore(2x-3)(x+1)=0_{}$