This lesson will look into how to divide a polynomial with another polynomial using long division.
Division of one polynomial by another requires a process somewhat like long division in arithmetic. Now, however, we will use polynomials instead of just numerical values.
The following diagram shows an example of polynomial division using long division. Scroll down the page for more examples and solutions on polynomial division.
Evaluate (x2 + 10x + 21) ÷ (x + 7) using long division.
(x2 + 10x + 21) is called the dividend and (x + 7) is called the divisor
Step 1: Divide the first term of the dividend with the first term of the divisor and write the result as the first term of the quotient.
Step 2: Multiply that term with the divisor.
Step 3: Subtract and write the result to be used as the new dividend
Step 4: Divide the first term of this new dividend by the first term of the divisor and write the result as the second term of the quotient.
Step 5: Multiply that term and the divisor and write the result under the new dividends.
Step 6: Subtract to get the remainder
Note that it also possible that the remainder of a polynomial division may not be zero.
Evaluate (23y2 + 9 + 20y3 – 13y) ÷ (2 + 5y2 – 3y)
You may want to look at the lesson on synthetic division (a simplified form of long division)Dividing Polynomials using Long Division
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