Quadratic Factoring 1

Algebra 1 Tutorial

Quadratic Factoring 1

Intro

Factoring quadratics is often an area where students struggle. In this tutorial I would like to go over the process for factoring the expression: (X^2 + X – 30)

Sample Problem

Factor the quadratic expression (X^2 + X – 30)

Solution

Begin by looking at the expression and know that your solution will be in the form of ( X ± _ )( X ± _ ). Notice that the expression is in the form of ( aX^2 + bX – c ), where ‘a’ is your leading coefficient, ‘b’ is your second coefficient and ‘c’ is your constant. Next, multiply the leading coefficient ( 1 ) by the constant ( -30 ). This will give you a value of ( -30 ); ignore the negative sign for now. Break the value of ( 30 ) down into its factors and list them…

( 1 , 30 )

( 2 , 15 )

( 3 , 10 )

( 5 , 6 )

Rewrite the expression and the solution form.

X^2 + X – 30 ——> ( X ± _ )( X ± _ )

Look above at the list of factors and choose the pair of numbers that will add to or subtract from each other to equal the same value as the second coefficient ( 1 ). This pair of numbers must also multiply to give you the same value as the constant in the original expression ( -30 ).

The pair of numbers above that will subtract from each other to equal ( 1 ) is the pair ( 5 , 6 ).

Apply the correct positive and negative signs —> ( -5 , 6 ). 6 – 5 = 1 , which is the value of your second coefficient. The pair ( -5 , 6 ) will also multiply together to give the value of ( -30 ), the value of the constant in the expression. The correct pair of numbers will add to or subtract from each other to give you the value of the second coefficient and will also multiply together to give the value of the constant.

Insert this pair of numbers into the solution form as follows below

( X – 5 )( X + 6 )

Your solution is **( X – 5 )( X + 6 )**

After arriving at your solution, always check your work. To do this, use the FOIL method on your solution to make sure you can reproduce the original expression.

( X – 5 )( X + 6 ) —> X^2 + 6X – 5X – 30 —> X^2 + X – 30

Your work checks out and is correct



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