Mathutoledoeduanderson1320 4 3 2 coeff x x 9 x

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Unformatted text preview: . We will use the Remainder Theorem and synthetic division to find q( 6 ) . 4 2 Coefficients 2 t −7 t +15 of 2 0 −7 0 15 12 2 72 390 2340 12 65 390 6 2355 Thus, q( 6 ) = 2355 ≠ 0 . Thus, by the Factor Theorem, t − 6 is not a factor of q( t ) = 2 t 4 − 7 t 2 + 15 . Example Find the value(s) of c so that x + 3 is a factor of f ( x ) = 2 x 4 − x 3 − 9 x 2 + 22 x + c . By the Factor Theorem, x + 3 is a factor of the polynomial f if and only if f ( − 3) = 0 . f ( − 3 ) = 162 + 27 − 81 − 66 + c = c + 42 Thus, f ( − 3 ) = 0 ⇒ c + 42 = 0 ⇒ c = − 42 . Using the Remainder Theorem and synthetic division to find f ( − 3 ) , we have Copyrighted by James D. Anderson, The University of Toledo www.math.utoledo.edu/~anderson/1320 4 3 2 Coeff x − x − 9 x 22 x c of 2 + + 2 −1 − 9 22 c −6 2 21 − 36 42 −7 12 − 14 −3 c + 42 By the Remainder Theorem, f ( − 3 ) =...
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