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practice on functions 1 solution guide-1

# practice on functions 1 solution guide-1 - New York...

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G. Lancer Page 1 New York Institute of Technology Mathematics Department M 141 Pre-Calculus Practice 1 - Solution Guide In order to conserve space and paper, the problems may not be done in proper numeric order. (1) Find the exact zeros of 4 2 ( ) 8 33 f x x x by factoring. 4 2 2 2 2 2 2 2 ( ) 8 33 0 ( 11)( 3) 0 11 0 3 0 11 3 11 3 3 : 11, 11, 3, 3 f x x x x x x x x x x x x i The four zeros are x x x i x i            (3) Completely factor 3 2 ( ) 5 7 4 6 f x x x x given that 1 i is a zero. (7) Use the Rational Zero Theorem to list all the possible rational zeros for the polynomial function 4 ( ) 4 7 10 f x x x   . 4 1 5 1 5 , , , 2 2 4 4 10 ( ) 4 7 10 4 : 1, 2, 5, 10, All the possible zeros of f x x x are factors of Factors are   With TI we find one real zero, 0.6 x   and since the other two zeros are 1 x i   and 1 x i   , then we can factor: 3 2 ( ) 5 7 4 6 ( 0.6)( (1 ))( (1 )) ( ) ( 0.6)( 1 )( 1 ) f x x x x x x i x i or f x x x i x i    

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