2. 4 x 2 − 4 x − 3 4 , bold italic x squared , minus 4 bold italic x minus 3

   • Step 1 Since there is no common factor, find ac.

     a c = 4 ( − 3 ) = − 12 eh c equals 4 open negative 3 close equals negative 12

     Think

     Do you need positive or negative factors?

     You need one negative factor and one positive factor.

   • Step 2 Since a c = − 12 < 0 , eh c equals negative 12 less than 0 comma  find factors of ac with opposite signs.

     Since b < 0 , b less than 0 comma  the factor with greater absolute value is negative.

     Factors of − 12 negative 12	1, − 12 negative 12	2, − 6 negative 6	3, − 4 negative 4
     Sum of factors	− 11 negative 11	− 4 negative 4	− 1 negative 1

   • Step 3 Factor the trinomial as follows.

     4 x 2 − 4 x − 3 4 x 2 + 2 x − 6 x − 3 Rewrite  b x  using  b = 2 − 6 . 2 x ( 2 x + 1 ) − 3 ( 2 x + 1 ) Find a common factor for the first two terms and another common factor for the last two terms. ( 2 x − 3 ) ( 2 x + 1 ) Rewrite using the Distributive Property. table with 4 rows and 1 column , row1 column 1 , 4 x squared , minus 4 x minus 3 , row2 column 1 , 4 x squared , plus 2 x minus 6 x minus 3 , column 2 cap rewrite , b x , using , b equals 2 minus 6 . , row3 column 1 , 2 x open 2 x plus 1 close minus 3 open 2 x plus 1 close , column 2 table with 2 rows and 1 column , row1 column 1 , cap find a common factor for the first two terms , row2 column 1 , and another common factor for the last two terms. , end table , row4 column 1 , open 2 x minus 3 close open 2 x plus 1 close , column 2 cap rewrite using the cap distributive cap property. , end table

   • Check ( 2 x − 3 ) ( 2 x + 1 ) = 4 x 2 + 2 x − 6 x − 3   = 4 x 2 − 4 x − 3 ✓ table with 2 rows and 2 columns , row1 column 1 , open 2 x minus 3 close open 2 x plus 1 close , column 2 equals , 4 x squared , plus 2 x minus 6 x minus 3 , row2 column 1 , , column 2 equals , 4 x squared , minus 4 x minus 3 check mark , end table

✓ Got It?

3. What is the expression in factored form? Check your answers.
   1. 4 x 2 + 7 x + 3 4 x squared , plus 7 x plus 3
   2. 2 x 2 − 7 x + 6 2 x squared , minus 7 x plus 6
   3. Reasoning Can you factor the expression 2 x 2 + 2 x + 2 2 x squared , plus 2 x plus 2  into a product of two binomials? Explain.

Take Note Key Concept: Factoring Perfect Square Trinomials