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Unformatted text preview: ) ( ) ( ) ( ) ( x r x q x d x f ! " # f = dividend d = divisor q = quotient r = remainder ! Example 1 Divide 7 11 3 2 2 3 ! $ $ x x x by 3 $ x . " ! Example 2 Divide 10 7 3 2 2 3 $ $ ! x x x by x x 2 2 $ . " If the divisor is of the form c x $ where c is a constant (positive or negative), then the long division process can be replaced by synthetic division . In synthetic division, only the coefficients are used. The quotient will always be one degree less than the dividend. ! Example 3 Use synthetic division to divide 6 7 3 $ $ x x by 2 ! x . " Remainder Theorem If the polynomial ) ( x f is divided by c x $ , then the remainder is equal to ) ( c f . ! Example 4 Given 3 5 4 3 ) ( 2 3 ! $ ! # x x x x f , use the Remainder Theorem to find ) 4 ( $ f . " Factor Theorem If ) ( # c f , then c x $ is a factor of ) ( x f . If c x $ is a factor of ) ( x f , then ) ( # c f . ! Example 5 Solve the equation 2 3 14 15 2 3 # $ $ ! x x x given that -1 is a zero of the function. "...
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