review 1 - polynomial functions - Review Questions Polynomial Functions Multiple Choice 1 10 ll 12 13 The minimum information required to determine the

review 1 - polynomial functions - Review Questions...

This preview shows page 1 - 6 out of 6 pages.

Image of page 1
Image of page 2
Image of page 3
Image of page 4
Image of page 5
Image of page 6

You've reached the end of your free preview.

Want to read all 6 pages?

Unformatted text preview: Review Questions — Polynomial Functions Multiple Choice 1. 10. ll. 12. 13. The minimum information required to determine the equation of a cubic function is: a all the zeros b. all the zeros and another point c. all the zeros, another point, and the sign of the first coefficient d. all the zeros, another point, the sign of the first coefficient, and the degree of the polynomial The equation fix) = k (x — SK): — 3:12 represents a cubic function: a. with two zeros c. with no turning point 13. with three zeros d. with three turning points . x5 + 5x + 2x3 + 3x2 + 4x4 + 6 arranged in descending order is: a. 6+5x+3xz+2x3+4x4+3:5 c. x5+4x4+2x3+3x2+5x+6 b. —(6 + 5x + 3x2 + 2x3 + 4x4 + x5) d. all of the above The division statement is: a. dividend x quotient + remainder = divisor b- divisor >< quotient + remainder = dividend 0- divisor >< dividend + remainder = quotient d. none of the above , A division has remainder 0. Which statement is true? a. The divisor and quotient are factors of the dividend. b. The divisor and remainder are factors of the quotient. c. The quotient and the dividend are factors of the divisor. d. The quotient and remainder are factors of the dividend. The divisor is x -« 3, the quotient is x + 2, and the remainder is l. The dividend is: a. x2—6 c. xz—x—S b. x2 — x — 6 d. 2x x + 2 is a factor of: a. x2+4x+4 C. x3+2x2—x—2 b. x2 — 4 d. all of the above A factor of x4 — 5x2 + 4 is: ' a. x — 2 C- 'a and b b. x w l d. neither a nor b The remainder is 1, the quotient is 2x + 3, and the dividend is 2x2 + 7x + 7. The divisor is: a. x~7 C. 2(x+7)+7 b. x+2 d. 2x2+7(x+1) The factors of x3 —- y3 are: a- ()6 ~y)(x2 + xy + yz) 0- (x ~y)(x + y)2 b- (x +y)(x2 — xy + yz) d- ()6 +y)(x —y)2 Which is a true statement regarding the factor theorem? a. x — k is a factor of fix) if and only if f(k) = 0 b. if x — b is a factor of g(x), then g(b) = 0 c. if Me) = 0, then x w c is a factor of h(x) d. all of the above Which is a true statement regarding the remainder theorem? a. when fix) is divided by x — k, then flk) = the remainder b. when g(x) is divided by jx — k, then g(j/k) = the remainder 0. a and b d. neither 21 nor b The roots of (x + l)():2 — x — 6) = O are: a. —1,1,—6,0 0: 4,—2.3 14. 15. 16. 17. 18. 19. 20. 13. 1,-1,—6 d. l,2,—3 The root(s) of x3 = 8 is (are): a. 2 c. 2, 2i, —2i b. 2, —2 d. 2, —2, 21' The roots of 2x3 = 18x are: a. 0, 2, 18 0. 0,2, 3, —3 b. 0, 2, —1 8 d. 0, 3, —3 All the roots of a polynomial equation are 0, 1, 2, and 3. The general equation is: a. k(x)(x+1)(x+2)(x+3)=0 c. k(x+ l)(x+2)(x+3)=0 b. k(x)(x — 1)(x - 2)(x — 3) = 0 d. k(x + 1)(x —- 2)(x - 3) = 0 The solution to (x — 5)(x + 5) > O is: a. [xl>5 I C. —5<x<5 b. [x|<5 d- —5£x35 The solution to (x2 ~ 1) S 0 is: a- 1x1>1 c. lx[<1 b» 1x121 d. mgr The solution to (x - 2)(x + 1) > 0 is: a. x < —1 C. x > 2 b. —1<x<2 d. x<—l andx>2 The cubic function is greater than the linear function when: —3.5 <x <—0.5 andx> 3 a. x<—2 andx> 1.43 c. b. —2<x<l.43 d. x<—3.5 and—0.5<x<3 21. fix) < 0 where the graph of fix) is: i a. above the x—axis c. between its zeros 13. below the x—axis d. outside its zeros Short Answer 22. Describe the interval(s) where each of the three functions is increasing. I 23.Match each graph with a description. a) increasing linear function b) constant linear function c) quadratic function with a local minimum d) quadratic function with a maximum e) cubic function with positive first coefficient f) cubic function with negative first coefficient 24. Describe the difference between a local maximum and a local maximum value. 25. Describe the behaviour of a function around a local minimum point. 26. Write f(x) = —2(x— 1)2(x+ 3) in expanded form. 27. Sketch the graph of fix) = (x — 3)(x + 2)(x + 5) using the zeros and end behaviours. 28. Determine the remainder r for (x + l)(x —- 2) + r = x2 —x + 7. 29. a) Divide x4 + x3 + 2x2 + l by x + 1 using synthetic division. b) Write the division statement. 30. st—l afactor ofx3 +2x2—6x+3? 31. Determine the remainder when x3 + 23c2 — 6x + l is divided by x + 2. 32. Use long division to divide 2x3 + 5x2 — 4x — 5 by 2x + l. 33. Use synthetic division to divide 2x3 + 5x2 — 4x — 5 by 2x + l 34. Factor x3 - 5x2 — x + 5. 35. Factor 4x3+4x2—x— l. 36. Factor x3 — 1000. 37. Factor x4 — 7x2 — 6x fully. 38. Solvex3—3x2—x+3=0. 39. Algebraically solve x(2x + l)(x — 4) > 0. 40. Determine the equation of the function with zeros at :1, —2, and y—intercept of ~6. Sketch the function using this information. 41. a) Without dividing, calculate the remainder when 4x4 —x3 + 2x2 — l is divided by 2x — l. b) Is 2x —1 a factor of4x4 ~x3 + 2x2 —— l? 42. Solve x3 — 3x2 + 5x — 3 = 0. Review Questions - Polynomial Functions (Units 1&2) Answer Section MULTIPLE CHOICE 1. B 2. A 3. C 4. B 5. A 6. C 7. D 8. C 9. B 10. A 11. D 12. A 13. C 14. C 15. D 16. B 17. A 18. D 19. D 20. C 21. B SHORT ANSWER 22. fix) increases for xeR; g(x) increases for x < 3; and h(x) increases for x < —1 and x > 2.5. ’23- flx) - 3); 3’06) ~ d); 1106) - e) 24. A local maximum is a point at which a curve changes from increasing to decreasing, whereas the local maximum value is the y-coordinate of that point. 25. When a function changes from decreasing to increasing, a local minimum occurs. 26. f(x)=—2x3—2x2+IUx-fi 27. Zerosare3,—2,and—5.k>0:>asx—>oo,f(x)—>oo 28. r = 9 29. a) x + 1 is the divisor :> k = —1 1x4+1x3+2x2+0x+1 i i J, J, i (remove literal coefficients) 1 l 2 0 l i :1 Q —_2 Z (multiply number at lower left by k) 1 0 2 3 (add) if it i 12 i (insert literal coefficients) 1x3 + 0x2 + 2x— 2 remainder 3 b) (x+ 1)(1x3+2x—2)+3 =x4 +x3+2x2 +1 30. yes 31. The remainder is 13. 2 x +2x—3 ) 3 2 32. 2x+1 2x +5x —4x—5remainder~2 l 33. 2x+l isthedivisor:>k=—— 2 29+ 5x2—4x—5 i J, \L i (remove literal coefficient) 2 5 —4 —5 i —_l —_2 ; (multiply number at lower left by k) 2 4 6 ~2 (add) i J! J/ i (+ 2, coefficient ofx in divisor) 1 2 —3 l i \L \L i (insert literal coefficients) lx2 + 2x — 3 remainder —2 34. x3—5x2—x+5=(x—l)(xm5)(x+1) 35. 4x3 +4x2—x— 1 =(2x— l)(2x+ l)(x+ 1) 36. x3 — 1000 =(x—10)(x2 +10x +100) 37. x4—7x2~6x =x(x+ l)(x—3)(x+ 2) 38. x=—1,l,3 39. x(2x+l)(x—4)>0 l The zeros of the corresponding equation are —— ,,0 and 4 —1_ sign of (2x + 1) sign 2of (x— 4) sign of product x(2x+1)(x~4)>0when—-2- <x<0andx>4. 40. The given zeros: f(x) = k(x — l)(x + l)(x + 2) y-intercept: flO) = —6 flO) = k(0 —1)(0 + l)(O + 2) —6 = k(-2) 3 = k fix) = 3(x -— l)(x + l)(x + 2) is the required function. I 41. a) When fix) is divided by 2x — 1, the remainder = ({5} fix)=4x4—x3+2x2—1 [I] [I] [I] [I] 1 1 I 3 f— =4 — — - +2 — —1=——-—+-—1=—— 2 16 8 4 4 8 2 8 3 Remainder = _E . 4 3 2 1 b)If2x—1 isafactor0f4x —x +2x —1,thenf :2: = 1 3 - 4 3 2 However,f E =—E,502x—1Isnotafactorofélx —x +2x ——1. 42. f(x)=x3—3x2+5x—3 f(1)=1—3+5—3=0=>x—1isafactor x2—2x+3 x— 1 ix} — 3x:’1 + 535— 3 remainder 0 (x—1)(x2—2x+3)=0 x—1=00rx2—2x+3=0 4:: «fez—4m: 2a i X=10TX=—““—"—" «hi—2f —4t1>(3> _——_.____—_ 2(1) I! ._.. 1+ N x=1,1+z’ 2 ...
View Full Document

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes