Lesson Vocabulary

• factoring by grouping

Problem 1 Factoring a Cubic Polynomial

What is the factored form of 3 n 3 − 12 n 2 + 2 n − 8 ? 3 n cubed , minus , 12 n squared , plus 2 n minus 8 question mark

3 n 3 − 12 n 2 + 2 n − 8 = 3 n 2 ( n − 4 ) + 2 ( n − 4 ) Factor out the GCF of each group of two terms.   = ( 3 n 2 + 2 ) ( n − 4 ) Factor out the common factor  n − 4 . Check  ( 3 n 2 + 2 ) ( n − 4 ) = 3 n 3 − 12 n 2 + 2 n − 8 ✓   table with 3 rows and 3 columns , row1 column 1 , 3 n cubed , minus , 12 n squared , plus 2 n minus 8 , column 2 equals , 3 n squared , open n minus 4 close plus 2 open n minus 4 close , column 3 cap factoroutthecap gcap ccap fofeachgroupoftwoterms. , row2 column 1 , , column 2 equals open , 3 n squared , plus 2 close open n minus 4 close , column 3 cap factoroutthecommonfactor . n minus 4 . , row3 column 1 , cap check , open , 3 n squared , plus 2 close open n minus 4 close , column 2 equals 3 , n cubed , minus , 12 n squared , plus 2 n minus 8 check mark , column 3 , end table

✓ Got It?

1. 1. What is the factored form of 8 t 3 + 14 t 2 + 20 t + 35 ? 8 t cubed , plus , 14 t squared , plus 20 t plus 35 question mark
   2. Reasoning How is the factoring method used in Problem 1 like the method used in Lesson 8-6? How is it different?