How to Factor Quadratic Expressions

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Learn how to factor quadratic expressions with Allison Moffett of the Mahalo Math Channel. Ms. Moffett shows how to break the expression apart and explains how to choose the sign to use in each factor. She determines the factors of the number 12 and decides which factor pair can be used to result in the correct x term. This education video is part of a larger series of math-related tutorials offered on the Mahalo.com YouTube channel.

A quadratic equation is one which can be
written in the form ax^2+ bx + c
= 0 with a, b, and c being real numbers and where a is not equal to zero.uncw.edu/courses/mat111hb/izs/asolve/asolve.html  If you know how to factor a quadratic
expression, you may try this method to solve a quadratic equation. When a factored
quadratic expression is set to zero, the resulting answer will produce two roots,
which can be checked to determine if they answer the equation.

Not all quadratic expressions can be factored but when the non-zero side of the equation can be factored, the results can be used to solve the problem. When
the equation cannot be factored, the equation may be solved by using the
principle of square roots, completing the square, or using the quadratic
equation.gpc.edu/~claiss/MathHandouts/solve quadratic methods.pdf   To prepare for factoring a quadratic expression, review relevant terms before beginning a problem. The first portion of the expression (x^2) is called the "squared term." The middle of the expression (x), which includes an x and a coefficient, is called the "x term." In cases where the x term does not have a visible coefficient, it can be rewritten as 1x, showing the understood coefficient of 1.  The final portion of the expression is a number and is called the constant.wtamu.edu/academic/anns/mps/math/mathlab/col_al… 

Step 1: Break the Expression into Pieces
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To factor a quadratic expression,
break
the expression into two binomials. Each binomial will receive an x and a constant.
Set up the binomials first by placing an "x" in each. For example, using the
quadratic expression x^2 - x -- 42, begin to factor by breaking the
expression into the following: 
   (
x±?) and (x±?)
Determine the sign of each binomial by
looking at the sign of the constant.
  In
this example, the constant is negative 42 (-42).  When a constant has a negative sign, one of
the two binomials will be positive and the other negative.youtube.com/watch?v=yfiMho1_t4k If the constant is
positive, both of the binomials will have the same sign.  When this is the case, the x term is used to
determine whether the sign is a plus or a minus.

Step 2: Factor the Constant
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Determine all the factors of the
constant. For the example
x^2 - x -- 42, because the constant is a negative number, one factor will be positive and
the other negative. Determine the numerical factor first and then
determine which sign combined with each part of the factor pair can be added or subtracted
to result in the coefficient of the x term.
For this example, the factors of 42 are 6 and 7, 2 and 21, and
1 and 42.

The
x term of the sample expression is -x (or -1x). The choice of 6
and 7, being one number apart, is the most likely choice for the correct factor
to use to result in a coefficient of 1.  Next, determine which of the (6,7) factor pair to make positive, and which should be negative.  The correct placement of sign will result in
negative 1 for an answer.
Positive 7 and
negative 6 yields a positive 1 answer which will not work for this expression. The correct signs to use for factors 6
and 7 in this example are -7 and +6.
 
Placing these in the binomials gives you (x-7) and (x+6) as factors.

Step 3: Check Using the FOIL Method
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Check your factorization by using the
FOIL method. FOIL is an acronym which defines the way of multiplying the
binomials. It can only be used for binomials.
 
The letters remind you what order to use to accomplish the multiplication.wtamu.edu/academic/anns/mps/math/mathlab/int_al… 
* Letter F stands for the first terms.
Multiply the first term of each binomial. Check the above example by
multiplying the
x from each binomial.* Letter O of the FOIL method multiplies the
outside terms....

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