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 \(\frac{4a^{3}  -  10a^{2}  +  5a}{2a}\)

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).

\(\frac{4a^{3}}{2a} - \frac{10a^{2}}{2a} + \frac{5a}{2a}\)

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.

= \(4a^{2} - 5a + \frac{5}{2}\)


Solve examples on division of polynomial by monomial:

1. Divide x6 + 7x5 – 5x4 by x2

= x6 + 7x5 – 5x4 ÷ x2

= \(\frac{x^{6}  +  7x^{5}  -  5x^{4}}{x^{2}}\)

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

= \(\frac{x^{6}}{x^{2}}  +  \frac{7x^{5}}{x^{2}} - \frac{5x^{4}}{x^{2}}\) 

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

= \(x^{4} + 7x^{3} - 5x^{2}\)


2. Divide a2 + ab – ac by –a

= a2 + ab – ac ÷ -a

= \(\frac{a^{2}  +  ab  -  ac}{-a}\)

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

= \(\frac{a^{2}}{-a}  +  \frac{ab}{-a}  -  \frac{ac}{-a}\)

= \(-\frac{a^{2}}{a}  -  \frac{ab}{a}  +  \frac{ac}{a}\)

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

= \(\frac{a^{3}  -  a^{2}b  -  a^{2}b^{2}}{a^{2}} \)

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

= \(\frac{a^{3}}{a^{2}}  -  \frac{a^{2}b}{a^{2}}  -  \frac{a^{2}b^{2}}{a^{2}}\)

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

= \(\frac{4m^{4}n^{4}  -  8m^{3}n^{4}  +  6mn^{3}}{-2mn}\)

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

 = \(\frac{4m^{4}n^{4}}{-2mn} - \frac{8m^{3}n^{4}}{-2mn} + \frac{6mn^{3}}{-2mn}\)

= \(-\frac{4m^{4}n^{4}}{2mn} + \frac{8m^{3}n^{4}}{2mn} - \frac{6mn^{3}}{2mn}\)

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

= 2m3n3 + 4m2n3 - 3n2







Algebra Page

7th Grade Math Problems

From Division of Polynomial by Monomial to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.