Given
[tex]2x^2-x-3=0[/tex]
How to factor
Solution
Step 1
Multiply the first and last costant
[tex]-3\times2x^2=-6x^2[/tex]
Step 2
Write out all the pair factors of -6x^2
[tex]\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}[/tex]
Step 3
Check for the pair, such that when you add you will get -x
[tex]\begin{gathered} it\text{ is } \\ -3x+2x=-x \\ \therefore-3x,\text{ 2x} \end{gathered}[/tex]
Step 4
Replace -x with -3x+2x in the equation
[tex]2x^2-3x+2x-3=0[/tex]
Step 5
Put them into brackets Since + is at the center no stress.
[tex](2x^2-3x)+(2x-3)=0[/tex]
Step 6
Factor out what is common in the bracket
[tex]x(2x^{}-3)+1(2x-3)=0[/tex]
Step 7
What is in the bracket are the same, pick one
[tex]\therefore(2x-3)(x+1)=0_{}[/tex]
