Problem 1 Dividing by a Monomial

What is ( 9 x 3 − 6 x 2 + 15 x ) ÷ 3 x 2 ? open 9 , x cubed , minus 6 , x squared , plus 15 x close divides 3 , x squared , question mark

( 9 x 3 − 6 x 2 + 15 x ) ÷ 3 x 2 = ( 9 x 3 − 6 x 2 + 15 x ) ⋅ 1 3 x 2 Multiply by  1 3 x 2 , the reciprocal of  3 x 2 .   = 9 x 3 3 x 2 − 6 x 2 3 x 2 + 15 x 3 x 2 Use the Distributive Property .   = 3 x 1 − 2 x 0 + 5 x − 1 Subtract exponents when dividing powers with the same base .   = 3 x − 2 + 5 x Simplify . table with 4 rows and 3 columns , row1 column 1 , open . 9 , x cubed , minus 6 , x squared , plus 15 x . close . divides 3 , x squared , column 2 equals . open . 9 , x cubed , minus 6 , x squared , plus 15 x . close . dot . fraction 1 , over 3 , x squared end fraction , column 3 cap multiplyby . fraction 1 , over 3 , x squared end fraction . comma . thereciprocalof . 3 , x squared , . , row2 column 1 , , column 2 equals . fraction 9 , x cubed , over 3 , x squared end fraction . minus . fraction 6 , x squared , over 3 , x squared end fraction . plus . fraction 15 x , over 3 , x squared end fraction , column 3 cap usethecap distributivecap property . . , row3 column 1 , , column 2 equals 3 , x to the first , minus 2 , x to the , plus 5 , x super negative 1 end super , column 3 table with 2 rows and 1 column , row1 column 1 , cap subtractexponentswhendividing , row2 column 1 , powerswiththesamebase . . , end table , row4 column 1 , , column 2 equals 3 x minus 2 plus , 5 over x , column 3 cap simplify , . , end table

The answer is 3 x − 2 + 5 x . 3 x minus 2 plus , 5 over x . .

✓ Got It?

1. Divide.
   1. ( 4 a 3 + 10 a 2 + 3 a ) ÷ 2 a 2 open 4 , eh cubed , plus 10 , eh squared , plus 3 eh close divides 2 , eh squared
   2. ( 5 b 4 − 15 b 2 + 1 ) ÷ 5 b 3 open 5 , b to the fourth , minus 15 , b squared , plus 1 close divides 5 , b cubed
   3. ( 12 c 4 + 18 c 2 + 9 c ) ÷ 6 c open 12 , c to the fourth , plus 18 , c squared , plus 9 c close divides 6 c