TERRA Environmental Research Institute



Alg 2 G CH 5 COMPREHENSIVE REVIEW CLASSWORK/HOMEWORK Section 5.1-5.6 ANSWER SHEET ONLY!!!- Do all your work on a separate sheet!!-ASSIGNMENT #____Use your own paper to work out each part, show work to the nth degree to ensure full credit , but more importantly to learn Chapter 5 in order to excel on your Chapter 5- Sec 5.1-5.6 Test!Last name:_______________________________ First:_______________ Per:________ NO graphing calculator allowed!!!!!!!. Use the g.c only to check your work after you have finished the entire problem!! PROBLEM #1) f(x)= 4x3-8x2-x+2a) Use the Rational Root Theorem to list the POSSIBLE Rational Roots of f(x)_____________________________________________________________________________________________b) List the ACTUAL rational roots of f(x) [Hint: Set f(x)=0, factor it using Grouping then DOS, then solve for x)_________ , _________ and ________c) According to Descartes’ Rule of sign, f(x) has how many POSSIBLE REAL ZEROS ? Number of Possible POSITIVE REAL zeros are:______________ Does it agrees with what you know about f(x) from previous parts?Number of Possible NEGATIVE REAL zeros are:______________ Does it agrees with what you know about f(x) from previous parts?d) Degree of f(x) = _____ Leading Coefficient is:______ End behavior of graph of f(x) is __________________Possible # of turning points of f(x) are:_________________________e) Compute( use your scientific calculator to compute these): f(-2)=_____, f(-1.5)=_____, f(-1)=______, f(-0.5)=______ , f(0)=______, f(.05)=______ f(1)=_____ f(1.5)=_______ , f(2)=_____ , f(2.5)=_______, f(3)=_______f) Now use part b, d and e to graph f(x) accurately, look at the list of points (part e) to determine a suitable scale for the y-axis. Graph f(x) accurately using. Do Not Use Graphing Calculator!!!g) List the coordinates of the x-intercepts graph paper _________________________________ and y-intercept______PROBLEM #2) g(x) = 6x4- 5x3- 12x2+ 5x +6 a) Use the Rational Root Theorem to list the POSSIBLE Rational Roots of f(x) [ there are many, list integers first, then fractions]________________________________________________________________________________________________b) Test your possible rational roots until you find one root, that is, an ACTUAL rational root of g(x), then use synthetic division to find the rest of the roots ( you need to use synthetic division twice!). Listen to instructionsActual roots are: _______, ________ , ________ and ________C) Now use part b to factor g(x) into linear factors, one factor per root. g(x) =______________________________________d) According to Descartes’ Rule of sign, g(x) has how many POSSIBLE REAL ZEROS ? Number of Possible POSITIVE REAL zeros are:______________ Does it agrees with what you know about g(x)from previous parts?Number of Possible NEGATIVE REAL zeros are:______________ Does it agrees with what you know about g(x)from previous parts? e) Degree of g(x) = _____ Leading Coefficient is:______ End behavior of graph of g(x) is __________________Possible # of turning points of g(x) are:_________________________f) Make a table of values then determine a suitable scale for your graph. g) Graph g(x) accurately using graph paper, use part d, and e to help you graph it correctly.PROBLEM #3 h(x)= -x4+12x2 -11a) Use the Rational Root Theorem to list the POSSIBLE Rational Roots of h(x) ________________________________________________________________________________________________b) Test your possible rational roots until you find one root, that is, an ACTUAL rational root of h(x), then use synthetic division to find the 2nd root (there are 2 rational roots). Actual rational roots are: _______, and ________ c) To find the remaining two roots, solve the quadratic polynomial you got on part b. The other two roots are _____ and _____ Circle all that applies: These 2 roots are: Irrational Real Complex Imaginaryd) Now use part b and c to factor h(x) over the indicated set:Factorization of h(x) over set of Rational numbers: ( ) ( ) ( )Factorization of h(x) over set of Real numbers: ( ) ( ) ( ) ( ) Factorization of h(x) over set of Complex numbers: ( ) ( ) ( ) ( ) e) According to Descartes’ Rule of sign, h(x) has how many POSSIBLE REAL ZEROS ? Number of Possible POSITIVE REAL zeros are:______________ Does it agrees with what you know about h(x)Number of Possible NEGATIVE REAL zeros are:______________ Does it agrees with what you know about h(x)f) Degree of h(x) = _____ Leading Coefficient is:______ End behavior of graph of h(x) is __________________Possible # of turning points of h(x) are:_________________________g) Make a table of values then determine a suitable scale for your graph based on these points.h) Graph h(x) accurately using graph paper, use part d, and e and a table of values ( select x-values to left and right of each x-intercept, to help you graph h(x) correctly. i) Set h(x)=0, multiply by -1, then factor trinomial into two quadratic factors, then solve for x.PROBLEM #4 k(x)= -2x3+x-6a) Use the Rational Root Theorem to list the POSSIBLE Rational Roots of k(x), and list the actual rational roots if any._____________________________________________________________________________________________b) According to Descartes’ Rule of sign, k(x) has how many POSSIBLE REAL ZEROS ? Number of Possible POSITIVE REAL zeros :___________ Number of Possible NEGATIVE REAL zeros:___________ c) Degree of k(x) = _____ Leading Coefficient is:______ End behavior of graph of k(x) is __________________Possible # of turning points of k(x) are:_________________________d) Make a table of value( use your scientific calculator to compute these): x-3-2.5-2-1.5-10.511.52ye) Now use part b, c and d to graph k(x) accurately, look at the list of points on the table to determine a suitable scale for the y-axis. Graph k(x) accurately using graph paper.f) According to your graph how many x-intercepts does k(x) have? _____ Is this x-intercept , a rational zero(root) or an irrational zero(root)? How do you know this?__________________________________________________________ g)According to the Fundamental Theorem of Algebra , how many complex roots does k(x) have?________ because the degree of this polynomial function is _____h)If k(x) has one irrational zero of multiplicity one, then the other two must be _____________ roots/zeros OR if K(x) does not have imaginary roots, then the irrational zero must be of multiplicity ____ (repeated root) i) If k(x) has two imaginary roots, they must be complex conjugates, why? Explain how you know this, be specific/precise & to the point!Add to Assignment #8 Comprehensive Review Sections 5.1-5.6 Show work in the space provided below each problem.Solve for x5) X3 + 27 =0 ( Hint: Factor using SOC technique, then solve for x)6) x4-26x2+25 =0 ( Hint: Factor trinomial using Trial and Error technique, keep on factoring until you have 4 factors, then solve for x)7) x4-11x2-12 =0 ( Hint: Factor trinomial using Trial and Error technique, solve for x2 then solve for x, don’t forget +/-)8) Divide using long division. Write your answer in proper form. 6x4- 5x3- 12x2+ 5x +6 ÷ ( x2 + 1)9) State the degree, find the zeros and state the multiplicity of each zero. P(x) = 5 x ( 2x + 1) 3 ( x – 7)2 ( x+ 9)10) Given P(x)= x4- 2x3+ 8x2-14x +7 a) find the missing quadratic factor if P(x)= x4- 2x3+ 8x2-14x +7 = (x2+7) ( ? ) ( Hint: Use long div.)b) Find the 4 roots of P(x) ................
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