Box Method for Factoring

Factoring expressions in the form of 2ax +bx+c

Box Method for Factoring

We are going to factor the expression First draw a box and divide into quarters.

215x -7x-2

Box Method for Factoring

Now we are going to place the terms of the expression into the box.

Look at the expression: Place the in the top left box. Place the -2 in the bottom right box.

215x -7x-2215x

215x

-2

Box Method for Factoring

Now we are going to multiply the coefficient of the first term by the constant. (15) (-2) = -30

215x -7x-2

215x

-2

Box Method for Factoring

Now we are going to list the factors of 30.

30

1 30

2 15

3 10

5 6 Are there any pair of numbers that would equal -7?

Box Method for Factoring We just found the factors of -30 that have

a sum of -7! We will place those factors in the box with

an “x” It doesn’t matter which box you put them

in.

215x

-2

-10x

3x

Box Method for Factoring

Now we are going to pull out the common factors from each row and column.

Last sign out of the box determines the sign.

215x

-2 3x

-10x

1

5x

3x -2

Box Method for Factoring

We now have the factors of The factors are: (5x + 1)(3x - 2)

215x -7x-2