Easy Algebra Step-by-Step

Factoring Polynomials 131

Step 4. Write the factored form.

35 xx^2555 x− 2 () 33 xx 11 ()x 2

f. 4 x^2 − 11 x− 3

Step 1. Because the expression has the form ax^2 +bx+c, look for two bino-

mial factors.

4 x^2 − 11 x − 3 = ( )( )

Step 2. 4 x^2 is the fi rst term, so the numerical coeffi cients of the fi rst terms

in the two binomial factors are factors of 4. The last term is −3, so

the last terms of the two binomial factors have opposite signs with

a product of −3. Try combinations of factors of 4 and −3 and check

with FOIL until the middle term is correct.

Tr y 41 xx^2111311 =()x ()

?

xx−

Check: () 23 x 3 () 212 x =+ 44 xxx^22226322636 xx 3 44444 x− 3

Wrong



Tr y 41 xx^2111311 =?()xxx ()x+

Check: () 43 x 3 ()x+ 1 44 xxx^222 + 43344333 xx 3 44444 x 3

Wrong



Tr y 41 xx^2111311 =?()xxx+ ()x−

Check: () 41 x (^1) ()x− 3 44 xxx^22121212 +−xxx 3434344 x − 11 x− 3
Correct

Step 3. Write the factored form.
41 xx^2111113 =() 414 x 1 ()x− 3
As you can see, getting the middle term right is the key to a successful
factorization of ax^2 +bx+c. You can shorten your checking time by sim-
ply using FOIL to compare the sum of the inner and outer products to the
middle term of the trinomial.
Factoring by Grouping
When you factor ax^2 +bx+c by grouping, you also guess and check, but in
a different way than in the previous method.
Problem Factor by grouping.
a. 4 x^2 − 11 x− 3
b. 9 x^2 − 12x + 4