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REVIEW UNIT 5 SOLUTIONS

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School
Saint James High**We aren't endorsed by this school
Course
MATHEMATICS 12345
Subject
Mathematics
Date
Dec 16, 2024
Pages
6
Uploaded by DeanSummer13687
©y r2o0M2h4s AKGumtQay _SvotfTtvwzawraeo FL]LeCx.h e JAoljlM SrJiOglhqtVsn Grxevske[rgvzendG.w a iMpaxdBe^ KwGiftnhP FI\nJfEirnnivtIes TAll_gveMbDrNah p2P.Worksheet by Kuta Software LLCAlgebra 2REVIEW UNIT 5 POLYNOMIALSName___________________________________ ID: 1Date________________ Period____©X g2q0c2n4I qKJuCtMaz XSCoYfZtEwiayrie[ dLJLhCV.M v wANlVlG JrLi_g]hvtZss MrQePsoeGrevmecd`.-1-1) How many zeros could the function f(x)= 2x5+ x3- 6x+ 1have?A) 4B) 3C) 2D) 5*2) If x+ 3is a factor of f(x), which of the following statements does NOT have to be true?A) -3 is a root of f(x).B) f(-3)= 0C) f(3)= 0*D) -3 is a zero of f(x).3) How many different third-degree polynomials have 3 and 1 as their only zeros?A) an infinite number*B) 3C) 1D) 0If the expression is a polynomial, then name each polynomial by degree and number of terms.If the expression is not a polynomial, then choose not a polynomial.4) 2x2- 3x+ 5A) quadratic trinomial*B) not a polynomialC) quadratic binomialD) linear trinomial5) 1*A) constant monomialB) quartic monomialC) quadratic monomialD) linear polynomial with 0 terms6) x5- 8x3+ 6x2A) quadratic monomialB) quintic binomial*C) quintic trinomialD) not a polynomial7) 5k4+ 4k-2- 8A) cubic polynomial with five termsB) quadratic monomial*C) not a polynomialD) quintic monomial8) 684A) constant trinomialB) quintic monomial*C) constant monomialD) not a polynomial9) 3b6A) constant monomialB) linear polynomial with six termsC) linear binomial*D) sixth degree monomial10) px3- 8x2+ 1A) quartic trinomialB) not a polynomial*C) cubic trinomialD) quadratic polynomial11) x3- 15x12- 11A) quartic trinomial*B) not a polynomialC) quadratic polynomialD) cubic binomial
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©s H2C0P2S4p hKfuttLaY QS^oGfWtcwJaRr^ef `LTLuCu.U v UALlml[ Tr\iwgGhJt`sg TraeosaesrqvYeudF.` b DMNafd\eu tw_ibtKhI zIznMf`iXnsiutbec kAJlogOexbPrmaR u2e.Worksheet by Kuta Software LLC-2-12) A quartic polynomial has, at most, how many turning points? A) 5B) 4*C) 3D) 113) What is the quotient when 9x4- 45x3+ 37x2+ x+ 2is divided by 9x2+ 1?A) x2- 5x+ 49x2+ 1+ 6x- 2B) x2+ x+ 29x2+ 1C) x2- 5x+ 4 + 6x- 29x2+ 1*D) x2- 5x+ 4Evaluate each function at the given value using synthetic substitution. SHOW YOUR WORK. 14) f(n)= 4n3+ 26n2+ 8n- 25at n= -6-115) f(n)= n3- 7n2+ 5n+ 16at n= 5-9
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©q y2w0D2`4\ \KnuxtJaS qSmoPfEtJwYaorEex DLCLrCu.Q ` uAelQlz ]rji^g^h[tYsj vrNe[sxevrov_egdw.Q ^ xMRaGdWew [wHiZtXhy KIUnhfWiBnoictneU [ADlHgcenbdrqaU W2`.Worksheet by Kuta Software LLC-3-Answer in COMPLETE sentences. 16) Based on this graph, what do you knowabout the leading coefficient and thedegree of this polynomial?xyThe degree is odd and the leading coefficient is positive.17) Based on this graph, what do you knowabout the exponent on the correspondingfactor at x= 1?xy-5-4-3-2-1123-6-5-4-3-2-1123The factor (x-1) has a multiplicity that is odd and greater than 1.18) How many turning points does thispolynomial have? What is the leastpossible degree of this polynomial basedon this graph?xy5 turning points; at least degree 8Simplify each difference.19) (b4+ 1 + 8b2)- (4b4+ 2 + 4b2)*A) -3b4+ 4b2- 1B) b4+ 4b2- 1C) b4+ 2b2- 1D) 2b4+ 4b2- 1
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©H g2^0U2Y4c ^K`uLtBaq HSyoAfFtHwJafrteH PLhL\Cw.^ _ HAHlglE erBiMgOhEtNs\ prieGsqeyrmvmefdJ.c i XM\agdUeH zwqi[tmhI UIDnqf`i_neiqtUea hAblngReobIroaU K2t.Worksheet by Kuta Software LLC-4-Divide. SHOW YOUR WORK.20) (-9x3- 88x2+ 18x- 22)¸(x+ 10)-9x2+ 2x- 2 - 2x+ 10Describe the end behavior of each function.21) f(x)= x2+ 4x+ 3A) Rises to the left. Falls to the rightB) Falls to the left. Rises to the rightC) Falls to the left. Falls to the right*D) Rises to the left. Rises to the right22) f(x)= x3- 4x2+ 3A) f(x)→+∞as x→-∞f(x)→-∞as x→+∞B) f(x)→+∞as x→-∞f(x)→+∞as x→+∞*C) f(x)→-∞as x→-∞f(x)→+∞as x→+∞D) f(x)→-∞as x→-∞f(x)→-∞as x→+∞23) f(x)= -x4+ 2x2+ 2A) f(x)→+∞as x→-∞f(x)→-∞as x→+∞B) f(x)→-∞as x→-∞f(x)→+∞as x→+∞*C) f(x)→-∞as x→-∞f(x)→-∞as x→+∞D) f(x)→+∞as x→-∞f(x)→+∞as x→+∞
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©O e2X0U2u4S FKTugtwak tSlovfXtmwJaQrpex YLxLKCb.E i dAUlOlR ^rYiSgvhFtcs[ `r\eisbeLrlvKekdl.a [ rMQavdleD jw_iHtwhT ^IonUfpiSnjiMtTec AAol\gEembUrCaX J2k.Worksheet by Kuta Software LLC-5-Find all zeros. One zero has been given.24) f(x)= x4- 2x3- x+ 2; 2{1, -1 + i32, -1 - i32, 2}Find all zeros.25) f(x)= 3x3- 3x2- 5x+ 5{1, 153, -153}26) f(x)= 5x4- 29x2- 42{7, -7, i305, -i305}
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©S Q2r0R2n4K nKAuntEaj VSkoSfMtRwgafrCe[ jLdLkCm.A u rAMlAl_ irYihglhatnsK lrleIsjeYr`vseRds.c X IMuaXdFew kwMiTtThP FIIn`fpisnliVtfeB LAulkgneebbriac m2e.Worksheet by Kuta Software LLC-6-27) x3- 5x2+ 7x- 3 = 0{3, 1mult. 2}Write a polynomial function of least degree with integral coefficients that has the given zeros.28) -23, 35, -14f(x)= 60x3+ 19x2- 23x- 629) -2 + 2, -3 + 3f(x)= x4+ 10x3+ 32x2+ 36x+ 1230) -2 - i, 2 - i, 2 + if(x)= x4- 6x2+ 25
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