·        Some quadratic expressions are the product of BIONOMIAL FACTORS.

Quadratic Trinomial                  Binomial Factors

    x² + 10x + 16              ( x + 2 ) ( x + 8 )

The diagram below shows how  x² + 10x + 16

can be displayed as a rectangle with sides of length

(x + 2)

and

(x + 8 .)

FOIL is a method used when multiplying polynomials

        F- First terms

        O- Outer terms

I- Inner terms

L- Last terms

( x + 2 ) ( x + 8 )                       * To factor trinomials of the form

                                                   x² + bx + c you can use FOIL

                                                with the strategy guess and

                                                 check.

The sum of the #’s   (outside x outside) + (inside * inside)

you see here

must equal b.

                         x² + bx + c = ( x + __ ) ( x + __ )

The product of the #’s  (last * last)

                                            you see here

                                                                               must equal c.

Example

Factor x² - 9x + 20

Choose numbers that are factors of 20. Look for a pair with a sum of –9.

Factors of 20                    Sum of Factors

-1 and –20                        -1 + ( -20 ) = -21

-2 and –10                        -2 + ( -10 ) = -12

-4 and –5                              -4 + (-5 ) = -9

List only negative factors because you are looking for a sum of –9.  Two positive numbers cannot have a negative sum.

The numbers –4 and –5 have a product of 20 and a sum of –9.  The correct factors are ( x – 5 ) and ( x – 4 ).

So,  x² -9x + 20 = ( x – 4 ) ( x – 5 ).