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.

Now the polynomials (4a

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:

= x

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

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.

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

= 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

= a

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

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 - b= 4m

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

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.

= 2m__7th Grade Math Problems__** **__From Division of Polynomial by Monomial to HOME PAGE__

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