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.
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)