Division Algorithm for Polynomials

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Dividing two numbersQuotient Divisor Dividend Remainder Which can be rewritten as a sum like this: Division Algorithm is Dividend = Divisor × Quotient + Remainder Quotient Divisor Dividend Remainder Dividing two Polynomials Let’s divide 3x2 + x − 1 by 1 + x We can write Dividend = Divisor × Quotient + Remainder 3x2 + x – 1 = (x + 1) (3x – 2) + 1 What if…We don’t divide? We divide 3x2 + x − 1 by x + 1 So, Dividend = Divisor × Quotient + Remainder 3x2 + x – 1 = (x + 1) × Quotient + Remainder Putting x = −1 3(−1)2 + (−1) – 1 = (−1 + 1) × Quotient + Remainder 1 = Remainder Remainder = 1