Division of Polynomial by Monomial

Division of polynomial by monomial means dividing the polynomials which is written as numerator by a monomial which is written as denominator to find their quotient.

For example: 4a3 – 10a2 + 5a ÷ 2a

Now the polynomials (4a3 – 10a2 + 5a) is written as numerator and the monomial (2a) is written as denominator.

Therefore, we get 4a310a2+5a2a

Now we observe that there are three terms in the polynomial so, each term of the polynomial (numerator) is separately divided by the same monomial (denominator).

4a32a10a22a+5a2a


Note:

The process is exactly converse of finding the L.C.M. of fractions and reducing the expression into a single fraction.

Now we will cancel out the common factor from both numerator and denominator to simplify.

4a25a+52


Solve examples on division of polynomial by monomial:

1. Divide x6 + 7x5 – 5x4 by x2

= x6 + 7x5 – 5x4 ÷ x2

= x6+7x55x4x2

Now, we need to divide each term of the polynomial by the monomial and then simplify.

= x6x2+7x5x25x4x2 

Now each term will be simplified by cancelling out the common factor.

= x4+7x35x2


2. Divide a2 + ab – ac by –a

= a2 + ab – ac ÷ -a

= a2+abaca

Now, we need to divide each term of the polynomial by the monomial and then simplify.

= a2a+abaaca

= a2aaba+aca

Now each term will be simplified by cancelling out the common factor.

= -a - b + c




3. Find the quotient a3 - a2b – a2b2 by a2

= a3 - a2b – a2b2 ÷ a2

= a3a2ba2b2a2

Now, we need to divide each term of the polynomial by the monomial and then simplify.

= a3a2a2ba2a2b2a2

Now each term will be simplified by cancelling out the common factor.

= a - b - b2



4. Find the quotient 4m4n4 – 8m3n4 + 6mn3 by -2mn

= 4m4n4 – 8m3n4 + 6mn3 ÷ -2mn

= 4m4n48m3n4+6mn32mn

Now, we need to divide each term of the polynomial by the monomial and then simplify.

 = 4m4n42mn8m3n42mn+6mn32mn

= 4m4n42mn+8m3n42mn6mn32mn

Now each term will be simplified by cancelling out the common factor.

= 2m3n3 + 4m2n3 - 3n2







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