Division of Polynomials
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Key Questions

It is the same but just instead of getting 0 you get a polynomial in the last step.
Divide
# 3x^3 â€“ 5x^2 + 10x â€“ 3 # by# 3x + 1# in this case you get a polynomial seven which can be writtten in algebraic terms as
#7x^0#
so this can be proved using the division algoritmdividend = divisor
#*# quotient + remainder 
The dividend and divisor are sorted in descending order related to x.
Divide the first term of the dividend by the first divider of x.This is the first term of the quotient.
Multiplied this term by each of the terms of the divisor and as these products have to subtract from dividing.These products with their signs changed the writing under the similar terms with them and make the dividend reduction.
The second term of the quotient. This must be multiplied by each of the terms of the divisor and subtract the product of the dividend.
We write these terms below their similar and by the reduction gives zero residue.
I do hope you can find it useful.

We divide each of the terms of the polynomial by the monomials separating the partial quotients with their own signs. This is the distributive law of division.
Example:
#3a^36a^2b+9ab^2 : 3a# #(3a^36a^2b+9ab^2) : 3a # =# (3a^36a^2b+9ab^2) /(3a)# =#(3a^3)/(3a)# #(6a^2b)/(3a)# +#(9ab^2)/(3a)# =#a^22ab+3b^2# I do hope you can find it useful.
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Videos on topic View all (2)
Rational Equations and Functions

1Inverse Variation Models

2Graphs of Rational Functions

3Division of Polynomials

4Excluded Values for Rational Expressions

5Multiplication of Rational Expressions

6Division of Rational Expressions

7Addition and Subtraction of Rational Expressions

8Rational Equations Using Proportions

9Clearing Denominators in Rational Equations

10Surveys and Samples