mac1105_lecture3_1 - L3 Polynomial Division Synthetic...

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21 L3 Polynomial Division; Synthetic Division Rational Expressions Long Division 15 426 426 15 = 426 = Check : Dividend = (Quotient)(Divisor) + Remainder Dividing by a monomial : 5 3 2 2 4 6 2 x x x x + = 2 2 x 5 3 2 4 6 x x x +
22 Dividing Two Polynomials with more than One Term : (1) Write terms in each polynomial in descending order according to degree. (2) Insert missing terms in both polynomials with a 0 coefficient. (3) Use Long Division algorithm. The remainder is a polynomial whose degree is less than the degree of the divisor. Example : Perform the division. 4 2 2 3 6 12 4 3 2 x x x x + = 2 3 0 2 x x + 4 3 2 3 0 6 12 4 x x x x + +
23 Synthetic Division Synthetic division is used when a polynomial is divided by a first-degree binomial of the form x k . 2 ax bx c x k + + k a b c Coefficients of Dividend Diagonal pattern : Multiply by k Vertical pattern : Add terms Example : Use synthetic division to find the quotient and remainder. 4 2 2 3 5 1 1 x x x x + + +
24 Example : Verify that 3 x is a factor of 3 2 10 6 x x x + Rational Expressions A
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