The Fundamental Theorem of Algebra Date Period

1 ] B2t0I1F6W `KTuDtGaK hS_oIfitbwCajrUeO o BAplvl^ ]rEi]gahztFsW _ vMsaSdkeZ _wtiKt^hZ LICnMf^iJnbiMtree mPerOeocDailscYublcuYs`.Worksheet by Kuta Software LLCKuta Software - infinite PrecalculusThe Fundamental Theorem of AlgebraName_____Date_____ Period____-1-State the number of complex zeros, the possible number of real and imaginary zeros, the possiblenumber of positive and negative zeros, and the possible rational zeros for each ) f(x) x x 2) f(x) x x x x x 3) f(x) x x x 4) f(x) x x x 5) f(x) x x x x x 6) f(x)

2 X x x x x State the possible rational zeros and an interval in which all real zeros lie for each function. Then factor each to linear and irreducible quadratic ) f(x) x x 8) f(x) x I c2]0E1I6m xKZurtbao jSlohfHttwCaSrHeB ^ f CAplAlw LrHimgEhwtvsB U rMDakd_er hwriftLhh AIKnVfCiHnJigtAe] BPBrCePcFaJlHcduFl^ by Kuta Software LLC-2-9) f(x) x x x x x 10) f(x) x x x x x 11) f(x) x x 12) f(x) x x Find all ) f(x) x x 14) f(x) x 15) f(x) x x x x x 16) f(x) x x 17) f(x) x x x x x 18) f(x) x x Factor each to linear factors.

3 One zero has been ) f(x) x x x x x ; c B2Y0C1K6i jKdujtraL aS[oxfPtTwXamrdec ZLGLXC\.j g gAclvlH vrziDg\hyt]sD ErLeYsgetrWv[ ^ BMvaudgeM dw[iFtcha YISnAfXilnCigtteE \PHr]eFc[aFlrcEu] by Kuta Software LLCKuta Software - infinite PrecalculusThe Fundamental Theorem of AlgebraName_____Date_____ Period____-1-State the number of complex zeros, the possible number of real and imaginary zeros, the possiblenumber of positive and negative zeros, and the possible rational zeros for each ) f(x) x x # of complex zeros: 4 Possible # of real zeros: 4, 2, or 0 Possible # of imaginary zeros.]

4 4, 2, or 0 Possible # positive real zeros: 1 Possible # negative real zeros: 1 Possible rational zeros: , , , , , , , , , 2) f(x) x x x x x # of complex zeros: 5 Possible # of real zeros: 5, 3, or 1 Possible # of imaginary zeros: 4, 2, or 0 Possible # positive real zeros: 0 Possible # negative real zeros: 5, 3, or 1 Possible rational zeros: , , , , , , , 3) f(x) x x x # of complex zeros: 3 Possible # of real zeros: 3 or 1 Possible # of imaginary zeros: 2 or 0 Possible # positive real zeros: 2 or 0 Possible # negative real zeros: 1 Possible rational zeros: , 4) f(x) x x x # of complex zeros: 3 Possible # of real zeros: 3 or 1 Possible # of imaginary zeros: 2 or 0 Possible # positive real zeros: 1 Possible # negative real zeros: 2 or 0 Possible rational zeros: , , 5) f(x) x x x x x # of complex zeros: 5 Possible # of real zeros: 5, 3, or 1 Possible # of imaginary zeros: 4, 2, or 0 Possible # positive real zeros.

5 5, 3, or 1 Possible # negative real zeros: 0 Possible rational zeros: , , , , , , , 6) f(x) x x x x x # of complex zeros: 5 Possible # of real zeros: 5, 3, or 1 Possible # of imaginary zeros: 4, 2, or 0 Possible # positive real zeros: 5, 3, or 1 Possible # negative real zeros: 0 Possible rational zeros: , , , , , , , , State the possible rational zeros and an interval in which all real zeros lie for each function. Then factor each to linear and irreducible quadratic ) f(x) x x Possible rational zeros: , , , , , Real zeros lie in: [ , ]Factors to: f(x) ( x )(x )(x )8) f(x) x Possible rational zeros: , , , Real zeros lie in: [ , ]Factors to: f(x) ( x )( x x ) u a2d0\1I6N CKkugt]an ESFobfvtvwWabrfeb ^ y vAjlal\ MrfiPgAhMt^s_ U _McaAdGeB CwXiGtthl KIYn`f`iPnEistleq zPQrAeXcNaPlhcZusl[ by Kuta Software LLC-2-9) f(x) x x x x x Possible rational zeros.

6 , , , , , , , Real zeros lie in: [ , ]Factors to: f(x) (x )(x )( x )10) f(x) x x x x x Possible rational zeros: , , , Real zeros lie in: [ , ]Factors to: f(x) (x )( x )(x )11) f(x) x x Possible rational zeros: , , , , , , , Real zeros lie in: [ , ]Factors to: f(x) ( x )(x )12) f(x) x x Possible rational zeros: , , , Real zeros lie in: [ , ]Factors to: f(x) (x )( x )Find all ) f(x) x x , , , 14) f(x) x , i , i 15) f(x) x x x x x , , , i , i 16) f(x) x x i, i, i , i 17) f(x) x x x x x , i , i , , 18) f(x) x x , , , Factor each to linear factors.

7 One zero has been ) f(x) x x x x x ; f(x) (x ) ( x )(x )(x )Create your own worksheets like this one with infinite Precalculus. Free trial available at