3 2 coeff 3 x 11x 22 x 6 of 3 11 22 6 trying

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Unformatted text preview: second quotient polynomial q 2 ( x ) = 3 x − 11 x − 22 x − 6 . We will use this polynomial to find the remaining zeros (roots) of f, including another zero (root) of 2. 3 2 Coeff 3 x − 11x − 22 x − 6 of 3 − 11 − 22 − 6 Trying 2 again: 6 − 64 −5 3 − 10 − 32 2 − 70 Thus, q 2 ( 2 ) = − 70 ≠ 0 ⇒ x − 2 is not a factor of the second quotient polynomial q 2 . Thus, 2 is a zero (root) of multiplicity 2 and ( x − 2 ) 2 is a factor of f. 3 Trying − 2 : 2 Coeff of 3x − 11x − 22 x − 6 3 − 11 − 22 − 6 −6 3 34 − 24 − 17 12 −2 − 30 q 2 ( − 2 ) = − 30 ≠ 0 ⇒ x + 2 is not a factor of the second quotient polynomial q 2 . However, − 2 is a lower bound for the negative zeros (roots) of Thus, q 2 (and f ) since we alternate from positive 3 to negative 17 to positive 12 to negative 30 in the third row of the synthetic division. 3 Trying 3: 2 Coeff 3 x − 11x − 22 x − 6 of 3 − 11 − 22 − 6 9 3 −6 − 84 −2 − 28 3 − 90 Thus, q 2 ( 3 ) = − 90 ≠ 0 ⇒ x − 3 is not a factor of q 2 (nor f ) and 3 is not a zero (root) of q 2 (n...
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