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

How do I factor the following equation in the link? It has been factored, but I need-example-1
User AyBayBay
by
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1 Answer

5 votes

Given


2x^2-x-3=0

How to factor

Solution

Step 1

Multiply the first and last costant


-3*2x^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_{}

User Dmitry Reutov
by
7.8k points

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