The box method is a visual way of factoring quadratic expressions. It changes a

quadratic expression from a trinomial to a product of two linear expressions. Thus

the box method factors a quadratic expression.

A quadratic equation must be in the standard form in order to solve it by the box

method. The LHS of a quadratic equation in the standard form is a quadratic expression

of the form of ax

p(x - q)(x - r) in the box method. The roots are calculated by applying the zero

product rule on the equation thus obtained.

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How to do the box method:

This section describes how the box method can solve quadratic equations. The quadratic

equation x

divided into six steps:

quadratic expression from a trinomial to a product of two linear expressions. Thus

the box method factors a quadratic expression.

A quadratic equation must be in the standard form in order to solve it by the box

method. The LHS of a quadratic equation in the standard form is a quadratic expression

of the form of ax

^{2}+ bx + c. This expression is factored to the formp(x - q)(x - r) in the box method. The roots are calculated by applying the zero

product rule on the equation thus obtained.

###
How to do the box method:

This section describes how the box method can solve quadratic equations. The quadraticequation x

^{2}+ 2x - 3 = 0 is solved by the box method. The working isdivided into six steps:

Step 1

Draw a box and divide it into four equal smaller boxes:

Step 2

- In box 1, write the first term x
^{2} - In box 4, write the third term -3

Step 3

Box 2 and box 3 are to be filled with terms such that the product of box 2 and box

3 equals the product of box 1 and box 4 and the sum of box 2 and box 3 equals the

middle (second) term of the quadratic, 2x.

3 equals the product of box 1 and box 4 and the sum of box 2 and box 3 equals the

middle (second) term of the quadratic, 2x.

- Product of box 1 and box 4 = -3x
^{2} - Middle (or second) term = 2x

- their product is -3x
^{2}, and - their sum is 2x

Step 4

Write the highest common factors (along with the signs) of each row to its left

and of each column on its top.

and of each column on its top.

Step 5

Take the two terms on the left of the box and make an algebraic expression by putting

a plus sign between them, that is, (x - 1).

Similarly, take the two terms on the top of the box and make an algebraic expression

by putting a plus sign between them, that is, (x + 3)

The product of these two algebraic expressions, (x - 1) and (x + 3) is equal to

the original quadratic expression. Thus the quadratic expression x

2x - 3 has been factored to (x - 1)(x + 3).

a plus sign between them, that is, (x - 1).

Similarly, take the two terms on the top of the box and make an algebraic expression

by putting a plus sign between them, that is, (x + 3)

The product of these two algebraic expressions, (x - 1) and (x + 3) is equal to

the original quadratic expression. Thus the quadratic expression x

^{2}+2x - 3 has been factored to (x - 1)(x + 3).

Step 6

Applying the Zero Product Rule to the quadratic equation (x - 1)(x + 3) = 0,

- Either (x - 1) = 0, whence x = 1
- Or (x + 3) = 0, whence x = -3

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