Algebra 1 : How to factor an equation

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #2371 : Algebra 1

Find the solutions to the following equation.

Possible Answers:

Correct answer:

Explanation:

The first step in solving the equation is to add  to both sides so that we can set the new equation equal to  so that we can factor it.

We now need to factor it. We need to find two numbers,  and , such that  and .

Those two numbers are 

Our new factored expression becomes

Now we can easily identify that the values that satisfy this equation are .

Example Question #11 : How To Factor An Equation

Solve by completing the square:

Possible Answers:

no real solution

Correct answer:

Explanation:

In order to set this up for completing the square, we need to move the 135 to the other side:

Now the equation is in the form:

To complete the square we need to add to both sides the folowing value:

So we need to add 9 to both sides of the equation:

Now we can factor the left side and simplify the left side:

Now we need to take the square root of both sides:

**NOTE: Don't foget to add the plus or minus symbol. We add this becase there are two values we can square to get 144:

 

and

**End note

Now we can split into two equations and solve for x:

and

So our solution is:

Example Question #12 : How To Factor An Equation

Factor:  

Possible Answers:

Correct answer:

Explanation:

There is a common variable  in each term.  Pull this out as a common factor.

Factor  .

The common factors that will achieve the middle term and will have a product of 36 is four and nine.  Write the binomials.

The cubics here cannot be simplified any further.

The answer is:  

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