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Chapter 12: Factorisation > Division of an Expression by a Monomial

Division of an Expression by a Monomial

Division of a polynomial by a monomial

Now, let's try doing the same method for longer and more complex equations. Consider the example consisiting of a trinomial divided by a monomial:

4y3+5y2+6y÷2y

We have:

4y3+5y2+6y = (2 × 2 × y × y × y) + (5 × y × y) + (2 × 3 × y)

We observe that is common amongst the first and the third term but not the second.

None the less we try to take 2y out as a common term. So,

4y3 + 5y2 + 6y = (2y) × (2 × y × y) + (2y) × (52 × y) + (2y) × 3

= 2y(2y2+ 52 × y + 3 )

On dividing by 2y we get:

= 2y2 + 52 × y + 3

which is the correct result.

An alternate method: Another way of doing division involving multiple terms is to divide all the individual terms with the denominator.

= 4y3+5y2+6y2y

= 4y32y+5y22y+6y2y

= 2y2+52y+3

which gives us the same answer.

Try These

Using the same method try to solve the following:

(i) 24xy2z3 by 6yz2

Instructions

24xy2z3÷6yz2

  • Between the numerator and denominator, cancel out the common factors
  • We get: keys="+ – × π ÷ brackets frac"
  • Cancelling out the common factors
  • Which gives us the above answer

(ii) 63a2b4c6 by 7a2b2c3

Instructions

63a2b4c6÷7a2b2c3

  • Between the numerator and denominator, cancel out the common factors
  • We get:
  • Cancelling out the common factors
  • Which gives us the above answer

Example 14: 24x2yz+xy2z+xyz2 by 8xyz

Method 1: Taking out the common factor from numerator and denominator

Instructions

24x2yz+xy2z+xyz2÷8xyz

  • We have the following
  • Taking out the common factors
  • We get:
  • Which gives us the above answer

Method 2: Dividing each term by denominator

Instructions

24x2yz+xy2z+xyz2÷8xyz

  • We have the following
  • Individually dividing each term by the denominator
  • We get:
  • Which gives us the same answer as earlier.