Intermediate Algebra chapter 5 part 3

Polynomial Division Chapter 5

Dividend, Divisor, Quotient, and Remainder Problems will look like dividend divisor or dividend ÷ divisor, where the dividend and divisor are polynomials. Problem and answer will look like dividend divisor = quotient + remainder divisor Check that the division has been performed correctly (i.e., the correct quotient and remainder have been found) by quotient · divisor + remainder = dividend That is, multiplying the quotient by the divisor and adding in the remainder has to result in the dividend.Example Problem: x2 + 5x + 9 x + 2 Dividend: x2 + 5x + 9 Divisor:  x + 2 Answer: x + 3 + 3 x + 2 Quotient: x + 3 Remainder: 3 Note that (x + 3)(x + 2) + 3 = x2 + 5x + 9, that is, quotient · divisor + remainder = dividend. Dividing a Polynomial by a Monomial To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.That means, apply the distibutive property and simplify. Example 3x2y + 5xy3 + 9 3xy =   3x2y 3xy   +   5xy3 3xy   +   9 3xy   =   x   +   5y2 3   +   3 xy Answer: 3x   +   5y2   +   3 xy Example a2b2c - 6abc2 + 5a3b5 2abc2 =   a2b2c 2abc2   -   6abc2 2abc2   +   5a3b5 2abc2   =   ab 2c   -   3   +   5a2b4 2c2 Answer: ab 2c   -   3   +   5a2b4 2c2 Long Polynomial Division Long polynomial division may always be used when the divisor has more than one term. That is, the divisor is a binomial or trinomial or etc. Long polynomial division is a technique for finding the quotient and remainder given the dividend and divisor. Long polynomial division is performed much like long division of numbers.