In this case, the division is exact and Dividend = Divisor x Quotient Long Division of Polynomials Example 1: Dividend Divisor Quotient In this case, the division is exact and Dividend = Divisor x Quotient

Dividend = Divisor x Quotient + Remainder Long Division of Polynomials Example 2: The number 7 when divided by 2 will not give an exact answer. We say that the division is not exact. [7 = (2 x 3) + remainder 1 ] In this case, when the division is NOT exact, Dividend = Divisor x Quotient + Remainder

Definition of degree: For any algebraic expression, the highest power of the unknown determines the degree. For division of polynomials, we will stop dividing until the degree of the expression left is smaller than the divisor. Algebraic Expression Degree 2x + 1 1 x3 - 5x 3 -3x2 + x + 4 2

Division by a Monomial Divide: Rewrite: Divide each term separately:

Division by a Binomial Divide: Divide using long division Insert a place holder for the missing term x 2

Division of Polynomials Division of polynomials is similar to a division sum using numbers. Consider the division 10 ÷ 2 = 5 Consider the division ( x2 + x ) ÷ ( x + 1 ) 5 2 10 - 10 -

Example 1: Example 2: - - - - -

3 2 7 6 1 When the division is not exact, there will be a remainder. - Consider the division 7 ÷ 2 Consider (2x3 + 2x2 + x) ÷ (x + 1) 3 2 7 - - 6 1 - remainder -1 remainder

Example 1: - - Degree here is not smaller than divisor’s degree, thus continue dividing - Degree here is less than divisor’s degree, thus this is the remainder

Example 2: - - Degree here is less than divisor’s degree, thus this is the remainder

Example 3: - -