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.
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 x^{6} + 7x^{5} – 5x^{4} by x^{2}= \(\frac{x^{6} + 7x^{5} - 5x^{4}}{x^{2}}\)
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.
= \(x^{4} + 7x^{3} - 5x^{2}\)
= \(\frac{a^{2} + ab - ac}{-a}\)
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
= \(\frac{a^{3} - a^{2}b - a^{2}b^{2}}{a^{2}} \)
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^{2}= \(\frac{4m^{4}n^{4} - 8m^{3}n^{4} + 6mn^{3}}{-2mn}\)
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^{3}n^{3} + 4m^{2}n^{3} - 3n^{2}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.
Apr 20, 24 05:39 PM
Apr 20, 24 05:29 PM
Apr 19, 24 04:01 PM
Apr 19, 24 01:50 PM
Apr 19, 24 01:22 PM