Easy Algebra Step-by-Step

Factoring Polynomials 127

b. ax+ by + ay + bx

Step 1. Rearrange the terms so that the fi rst two terms have a common fac-

tor and the last two terms have a common factor, and then group the

terms in pairs accordingly.

ax++byby ay+bx

=+ax bx++ay by

=(abxx++b)+()++

Step 2. Factor the common factor x out of the fi rst term and the common

factor y out of the second term.

=xy( b)+y(ab+ )

Step 3. Determine the GCF for x(a+b) and y(a+b).

GCF = (a+b)

Step 4. Use the distributive property to factor (a + b) from the expression.

x(a + b) + y(a + b)

= (a + b)(x + y)

Factoring Quadratic Trinomials

When you have three terms to factor, you might

have a quadratic trinomial of the form ax^2 + bx + c.

It turns out that not all quadratic trinomials are

factorable using real number coeffi cients, but many

will factor. Those that do will factor as the product

of two binomials.

Two common methods for factoring ax^2 +bx+ c are factoring by trial and

error and factoring by grouping.

Factoring by Trial and Error Using FOIL

When you factor by trial and error, it is very helpful to call to mind the FOIL

method of multiplying two binomials. Here is an example.

() 25 x 5 () 343 x

= 23 xx⋅ 3 + 24 xx⋅⋅ 4 ++ 5353 ⋅ + 54 ⋅

First Outer ILe ast

   

= 68 xx^2 ++ 8 ++ 15 x 20

Middle terms



= 62 xx^2 ++ 2323 + 0

You should recall (from Chapter 9)

that quadratic trinomials result

when you multiply two binomials.