Algebra Demystified 2nd Ed

Chapter 6 FaCtoring and the distributive ProPerty 155

EXAMPLES

Determine whether to begin the factoring as (x + __ )(x + __ ), (x – __ )(x – __ ),

or (x – __ )(x + __ ).

x^2 – 4x – 5 = (x – __ )(x + __ ) or (x + __ )(x – __ )

x^2 + x – 12 = (x + __ )(x – __ ) or (x – __ )(x + __ )

x^2 – 6x + 8 = (x – __ )(x – __ )

x^2 + 4x + 3 = (x + __ )(x + __ )

PRACTICE

Determine whether to begin the factoring as (x + __ )(x + __ ), (x − __ )(x − __ ),

or (x − __ )(x + __ ).

1. x^2 − 5x − 6 =


2. x^2 + 2x + 1 =


3. x^2 + 3x − 10 =


4. x^2 − 6x + 8 =


5. x^2 − 11x − 12 =


6. x^2 − 9x + 14 =


7. x^2 + 7x + 10 =


8. x^2 + 4x − 21 =

✔SOLUTIONS

1. x^2 − 5x − 6 = (x − )(x + )


2. x^2 + 2x + 1 = (x + )(x + )


3. x^2 + 3x − 10 = (x − )(x + )


4. x^2 − 6x + 8 = (x − )(x − )


5. x^2 − 11x − 12 = (x − )(x + )


6. x^2 − 9x + 14 = (x − )(x − )


7. x^2 + 7x + 10 = (x + )(x + )


8. x^2 + 4x − 21 = (x − )(x + )

Once the signs are determined all that remains is to fill in the two blanks. We
look at all of the pairs of factors of the constant term. These pairs will be the
candidates for the blanks. For example, if the constant term is 12, we need to

EXAMPLES

Determine whether to begin the factoring as (

PRACTICE

Determine whether to begin the factoring as (