Lesson Vocabulary

• Zero-Product Property

Take Note Property Zero-Product Property

For any real numbers a and b, if a b = 0 , eh b equals 0 comma  then a = 0  or  b = 0 . eh equals 0 , or , b equals 0 .

Example If ( x + 3 ) ( x + 2 ) = 0 , open x plus 3 close open x plus 2 close equals 0 comma  then x + 3 = 0 x plus 3 equals 0  or x + 2 = 0 . x plus 2 equals 0 .

Problem 1 Using the Zero-Product Property

What are the solutions of the equation ( 4 t + 1 ) ( t − 2 ) = 0 ? open 4 t plus 1 close open t minus 2 close equals 0 question mark

( 4 t + 1 ) ( t − 2 ) = 0 4 t + 1 = 0 or t − 2 = 0 Use the Zero-Product Property . 4 t = − 1 or t = 2 Solve for  t . t = − 1 4 or t = 2   table with 2 rows and 1 column , row1 column 1 , open , 4 t plus 1 , close . open , t minus 2 , close . equals 0 , row2 column 1 , table with 3 rows and 6 columns , row1 column 1 , 4 t plus 1 , column 2 equals 0 , column 3 or , column 4 t minus 2 , column 5 equals 0 , column 6 cap usethecap zerominuscap productcap property . . , row2 column 1 , 4 t , column 2 equals negative 1 , column 3 or , column 4 t , column 5 equals 2 , column 6 cap solvefor . t . , row3 column 1 , t , column 2 equals negative , 1 fourth , column 3 or , column 4 t , column 5 equals 2 , column 6 , end table , end table