is there any method used in division of polynomials to find the remainder without doing actual division method, if yes mention the steps
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Arithmetic operations like addition, subtraction, multiplication and division play a huge and most basic rule in Mathematics. Maths is made by these operations. All other operations go easy with the polynomials except the division operation, which gets complex when dealt with polynomials. But this section will explain to you the division of polynomials and the division algorithm related to it, from basics.So, what’s the basic formula we are learning from the day we solved our first division problem? This is:
Dividend = Quotient × Divisor + Remainder
Step-by-step explanation:
Example: Divide the polynomial 2x2+3x+1 by polynomial x+2.
Solution: Divisor= x+2
Dividend=2x2 + 3x + 1
Note: Put the dividend under the division sign and divisor outside the sign.SIGNUP
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Value of Polynomial and Division Algorithm
Arithmetic operations like addition, subtraction, multiplication and division play a huge and most basic rule in Mathematics. Maths is made by these operations. All other operations go easy with the polynomials except the division operation, which gets complex when dealt with polynomials. But this section will explain to you the division of polynomials and the division algorithm related to it, from basics.
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So, what’s the basic formula we are learning from the day we solved our first division problem? This is:
Dividend = Quotient × Divisor + Remainder
Example: Divide the polynomial 2x2+3x+1 by polynomial x+2.
Solution: Divisor= x+2
Dividend=2x2 + 3x + 1
Note: Put the dividend under the division sign and divisor outside the sign.
Division Algorithm
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Steps for Division of Polynomials
Step 1: Firstly, Arrange the divisor as well as dividend individually in decreasing order of their degree of terms.
Step 2: In case of division we seek to find the quotient. To find the very first term of the quotient, divide the first term of the dividend by the highest degree term in the divisor. In the current case,
2x2/x = 2x.
Step 3: Write 2x in place of the quotient.
Step 4: Multiply the divisor by the quotient obtained. Put the product underneath the dividend.
Step 5: Subtract the product obtained as happens in case of a division operation.
Step 6: Write the result obtained after drawing another bar to separate it from prior operations performed.
Step 7: Bring down the remaining terms of the dividend.
Step 8: Again divide the dividend by the highest degree term of the remaining divisor. Follow the same prior procedure until either the remainder becomes zero or its degree is less than the degree of the divisor.
Step 9: At this stage, the quotient obtained is our answer.
Quotient Obtained = 2x + 1
Note: Division Algorithms for Polynomials is same as the Long Division Algorithm In Polynomials