Part 2
1. What is the leading coefficient of a polynomial function?
A) the coefficient of the term with the highest exponent
B) the constant term in the polynomial
C) the term with the lowest exponent
D) the coefficient of the quadratic term

2. Which of the following is true about a polynomial of degree 1?
A) It has at most one zero
B) It has exactly one zero
C) It has at most two zeros
D) It has an infinite number of zeros

3. What does the Location Theorem state about zeros of a polynomial function?
A) It guarantees the existence of at least one zero within an interval
B) It provides a method to factorize polynomials
C) It predicts the exact location of all zeros
D) It specifies the domain of the polynomial function

4. The Rational Root Theorem states that if q/p is a rational root of a polynomial function, then:
A) q is a factor of an and p is a factor of a0
B) q is a factor of a0 and p is a factor of an
C) q is a factor of the constant term and p is a factor of the leading coefficient
D) q is a factor of the leading coefficient and p is a factor of the constant term

5. The Fundamental Theorem of Algebra states that:
A) Every polynomial has at least one real root
B) Every polynomial has at least one complex root
C) Every polynomial has at least one imaginary root
D) Every polynomial has at least one rational root

6. Which theorem allows us to recognize the relationship between factors of a polynomial and its zeros?
A) Factor Theorem
B) Remainder Theorem
C) Conjugate Roots Theorem
D) Location Theorem

7. The Factor Theorem states that x - r is a factor of a polynomial p(x) if:
A) p(r) = 0
B) p'(x) = r
C) p''(r) = 0
D) p(r) = 1

8. How do you find the zeros of a polynomial using the Remainder Theorem?
A) By checking if the remainder is greater than zero
B) By substituting x = 0 into the polynomial
C) By dividing the polynomial by (x - r) and evaluating p(r)
D) By differentiating the polynomial

9. According to the Conjugate Roots Theorem, if 1 - 3i is a zero of a polynomial, what must also be a zero?
A) 1 + 3i
B) 1 + 2i
C) 1 - 2i
D) 1 - i

10. What does the Factor Theorem establish regarding zeros of a polynomial?
A) The relation between factors of a polynomial and its zeros
B) The existence of only real roots for a polynomial
C) The exclusivity of complex roots for a polynomial
D) The dominance of irrational roots over rational roots

11. The Rational Function (f(x) = n(x)/d(x)) is defined as:
A) a function expressed as the ratio of two polynomials
B) a function with only linear terms
C) a function with a constant denominator
D) a function with a quadratic numerator

12. In a polynomial of degree n, how many zeros can it have at most?
A) n
B) n - 1
C) n + 1
D) Two

13. The Linear Factorization Theorem states that a polynomial of degree n can be expressed as:
A) n linear factors
B) n quadratic factors
C) n cubic factors
D) n quartic factors

14. What is the Domain of a rational function f(x) = n(x)/d(x)?
A) {x : d(x) ≠ 0}
B) {x : n(x) ≠ 0}
C) {x : f(x) ≠ 0}
D) {x : n(x) = 0}

15. How many zeros does a polynomial of degree 3 have, as per the Linear Factorization Theorem?
A) 1
B) 2
C) 3
D) 4

16. The Remainder Theorem is based on the divisibility of:
A) p'(x)
B) (x - r)
C) q'(x)
D) (x + r)

17. What is the standard form of a polynomial function of degree 3?
A) an x^3 + an-1 x^2 + ... + a0
B) ax^3 + bx^2 + cx + d
C) (x - r1)(x - r2)(x - r3)
D) a3 x^3 + a2 x^2 + a1 x + a0

18. How do you find the remainder when p(x) = x^3 - x^2 + 3x - 1 is divided by x - 2?
A) p(2)
B) p'(2)
C) p(3)
D) p'(3)

19. According to the Factor Theorem, x - r is a factor of p(x) if:
A) p(r) = 0
B) p(r) = 1
C) p'(r) = 0
D) p''(r) = 0

20. What theorem can be used to find at least one zero of a polynomial within a specified interval?
A) Conjugate Roots Theorem
B) Location Theorem
C) Rational Root Theorem
D) Factor Theorem

Answer
1. B) The leading coefficient
2. B) Quadratic function
3. B) q(x) = 3x^4 + 2x - π
4. D) Forms a smooth unbroken curve
5. B) 2
6. C) 3
7. D) Increasing y-values
8. D) The roots of the polynomial equation p(x) = 0
9. D) The remainder after division
10. C) The roots or zeros of p(x)
11. C) r is a root of the polynomial equation p(x) = 0
12. B) The weights given to different terms
13. B) One less than its degree
14. C) 2
15. C) By solving the equation p(x) = 0
16. B) The end behavior of the function
17. C) Quintic function
18. A) Determines the location of the origin on the graph
19. B) At most n - 1 turning points
20. C) The domain of a polynomial function is always the set of real numbers

Economic final Ddu
1, https://t.me/tumimfamil/391?single
2, https://t.me/tumimfamil/407?single
3, https://t.me/tumimfamil/419?single

Chersachu simut

💞💞💞በምክንያት ነዉ
ትላንትናችን ላይ የተደረጉት ነገሮች ዛሬያችን ላይ ሊያስደረጉን የሚችሉበትን አቅም በኛ ይወልዳሉ አንዳንድ ምክንያቶች ትላንታችን ላይ የተደረጉበት ሁነኛ ሚስጥር ዛሬያችን ላይ ለምናደርጋቸው ብቃት መወለጃ ናቸው።
👦ሰዉ ሆይ ምክንያቶች ያለ ምክንያት አይኖሩም
ተደራግ ምክንያቶች ጀርባቸው ላይ አስደረጊ ምክንያቶች አላቸው ዛሬ ለምናደርጋቸው ምክንያቶች አስደናቂ ምክንያቶቻችን ትዝታ ውስጥ ገብተን ልናደርግ የቻልነው። በኛነታችን በስብእናችን በፍላጎታችን ሳይሆን ትላንታችንን የተቀላቀለው ምክንያት ዛሬያችን ላይ የምናደርጋቸውን ምክንያቶች  ወልዷል ስለዚህ ምክንያቶች ምክንያት አላቸው።
ኃላ የለለዉ ፍት የለዉም
ትላንት የለለዉ ዛሬ የለዉም
ለዝህም መፅሐፍ ቅዱስ
ሲናገር የተቆረጥክበትን ድንጋይ ደግሞ የተማስክበትን ጉድጓድ ወደ ኋላ ሄደህ አባትህን አብርሃም እናትህን ሳራ  ተመልከት ይላል። ትላንት ካላቹ ነገ አላቹ  ስለዚህ ብዙ ምክንያቶች የህይወት አለማችን ላይ ተቀዛቅዘዉብን ከሆነ ልንሆን የምንፈልጋቸውን ነገሮች ባለመሆን ከድነናቸው ከሆነ መሯሯጥ የምንችልባቸውን አቅሞች ወደ ዳር ጥለናቸው ከሆነ
ትላንትናችን ላይ የተሯራጠልን ለላ አቅም እንዳለ እየረሳን ነው ማለት ነው።የሕይወት ዓለማችን በድብዛዘ ከተሞላ
ዛሬ ጎላጎላ እንዲል ወደ ትላንትና እናያለን ዛር ብለን የምናየው ቀና ብለን እንድናይ አቅም ይወልድልናል።
ትላንት አናልፍም ብለን ተስፋ የቆረጥን የተከፋን  ቀን እና ለልቶች  ነበሩ:: የእግዚአብሔር ክንድ 💪💪  ብርታታችን ሆኖ ያለፍናቸዉ::
እና ዛሬ የደከመ ከመሰላቹ ወደ ትላንትናቹ እዩ
አሁን ላይ በራሳችን ልንሰራ እየሞከርን ይሆናል
ለሰው የማይቻል ለእግዚአብሔር ይቻላል።

ራእይ 2
4 የቀደመውን ፍቅርህን ትተሃልና።

Economics

Economic work sheet

Global trends Final Ddu
https://t.me/diredawa2015/181?single

NB.There is no any gap between Global and Anthropology .we will take anthropology exam after tomorrow ,


ምንም በመሃል gap የለም፣አረጋግጠናል