Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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Concept explainers

Polynomials
Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.
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Chapter 5.8, Problem 44WE
To determine

To find : two negative values of k for which the given polynomial can be factored

Expert Solution & Answer
Check Mark

Answer to Problem 44WE

The two negative values of k for which k−6z+z2   can be factored are : −7  &  −16

Explanation of Solution

Given information : k−6z+z2  

Concept Involved:

Whenever we have a trinomial of the form ax2+bx+c , follow the below steps to factor it ac or grouping method

  1. Identify the SUM { b } and PRODUCT { ac } of the expression
  2. Find two factors two rewrite the middle term m and n in such a way that it is multiplied to give PRODUCT and added to give the SUM of the expression.
    3. {Hint: List the factor pair of ac and see which two factors add up to give b to get the numbers m and n .}
  3. Use the two numbers m and n to rewrite the middle term to look as ax2+mx+nx+c
  4. Factor the GCF of first two terms and factor the GCF of last two terms. {Note: we will end up getting common binomial after this step}
  5. Factor the common binomial from the whole expression to get the final factored expression.

The condition for the trinomial of the form ax2+bx+c to be factored

  • The coefficient of middle term is equal to the sum of factor pairs of ac

    • Calculation:

    Rewrite the given expression k−6z+z2   in the form ax2+bx+c

      z2−6z+k 

    Identify the a, b and c of the given expression z2−6z+k 

      a=1;  b=−6;  c=k

    Identify the SUM { b } and PRODUCT { ac } of the expression

      SUM=−6;     

      PRODUCT=k

    When we think of two numbers m & n that add up to give -6 and have a negative product.

    To get a negative product one of the factors need to be positive and one of them need to negative.

    To get -6 as sum, the larger number out of two need to be negative.

    We need to pick m & n in such a way that m+n=−6 and k=m⋅n

    Possible two numbers that add up to -6 are:

    1. {m,n}⇒{−7, 1} . So k=−7⋅1=−7
    2. {m,n}⇒{−8, 2} . So k=−8⋅2=−16

    Conclusion:

    Listing the two trinomial that can be factored by replacing the k values:

    1. z2−6z−7
    2. z2−6z−16

    The two negative values of k for which z2−6z+k  can be factored are : −7  &  −16

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    Chapter 5.8, Problem 43WE
    Next
    Chapter 5.8, Problem 45WE

    Chapter 5 Solutions

    Algebra: Structure And Method, Book 1

    Ch. 5.1 - Prob. 1OECh. 5.1 - Prob. 2OECh. 5.1 - Prob. 3OECh. 5.1 - Prob. 4OECh. 5.1 - Prob. 5OECh. 5.1 - Prob. 6OECh. 5.1 - Prob. 7OECh. 5.1 - Prob. 8OECh. 5.1 - Prob. 9OECh. 5.1 - Prob. 10OE
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Prob. 45WECh. 5.6 - Prob. 46WECh. 5.6 - Prob. 47WECh. 5.6 - Prob. 48WECh. 5.6 - Prob. 49WECh. 5.6 - Prob. 50WECh. 5.6 - Prob. 51WECh. 5.6 - Prob. 52WECh. 5.6 - Prob. 53WECh. 5.6 - Prob. 54WECh. 5.6 - Prob. 55WECh. 5.6 - Prob. 56WECh. 5.6 - Prob. 57WECh. 5.6 - Prob. 58WECh. 5.6 - Prob. 59WECh. 5.6 - Prob. 60WECh. 5.6 - Prob. 61WECh. 5.6 - Prob. 62WECh. 5.6 - Prob. 63WECh. 5.6 - Prob. 64WECh. 5.6 - Prob. 65WECh. 5.6 - Prob. 66WECh. 5.6 - Prob. 1MRECh. 5.6 - Prob. 2MRECh. 5.6 - Prob. 3MRECh. 5.6 - Prob. 4MRECh. 5.6 - Prob. 5MRECh. 5.6 - Prob. 6MRECh. 5.6 - Prob. 7MRECh. 5.6 - Prob. 8MRECh. 5.6 - Prob. 9MRECh. 5.6 - Prob. 10MRECh. 5.6 - Prob. 11MRECh. 5.6 - Prob. 12MRECh. 5.6 - Prob. 1STCh. 5.6 - Prob. 2STCh. 5.6 - Prob. 3STCh. 5.6 - Prob. 4STCh. 5.6 - Prob. 5STCh. 5.6 - Prob. 6STCh. 5.6 - Prob. 7STCh. 5.6 - Prob. 8STCh. 5.6 - Prob. 9STCh. 5.6 - Prob. 10STCh. 5.6 - Prob. 11STCh. 5.6 - Prob. 12STCh. 5.7 - Prob. 1OECh. 5.7 - Prob. 2OECh. 5.7 - Prob. 3OECh. 5.7 - Prob. 4OECh. 5.7 - Prob. 5OECh. 5.7 - Prob. 6OECh. 5.7 - Prob. 7OECh. 5.7 - Prob. 8OECh. 5.7 - Prob. 9OECh. 5.7 - Prob. 10OECh. 5.7 - Prob. 11OECh. 5.7 - Prob. 12OECh. 5.7 - Prob. 13OECh. 5.7 - Prob. 14OECh. 5.7 - Prob. 15OECh. 5.7 - Prob. 16OECh. 5.7 - Prob. 17OECh. 5.7 - Prob. 18OECh. 5.7 - Prob. 19OECh. 5.7 - Prob. 20OECh. 5.7 - Prob. 21OECh. 5.7 - Prob. 22OECh. 5.7 - Prob. 23OECh. 5.7 - Prob. 24OECh. 5.7 - Prob. 25OECh. 5.7 - Prob. 1WECh. 5.7 - Prob. 2WECh. 5.7 - Prob. 3WECh. 5.7 - Prob. 4WECh. 5.7 - Prob. 5WECh. 5.7 - Prob. 6WECh. 5.7 - Prob. 7WECh. 5.7 - Prob. 8WECh. 5.7 - Prob. 9WECh. 5.7 - Prob. 10WECh. 5.7 - Prob. 11WECh. 5.7 - Prob. 12WECh. 5.7 - Prob. 13WECh. 5.7 - Prob. 14WECh. 5.7 - Prob. 15WECh. 5.7 - Prob. 16WECh. 5.7 - Prob. 17WECh. 5.7 - Prob. 18WECh. 5.7 - Prob. 19WECh. 5.7 - Prob. 20WECh. 5.7 - Prob. 21WECh. 5.7 - Prob. 22WECh. 5.7 - Prob. 23WECh. 5.7 - Prob. 24WECh. 5.7 - Prob. 25WECh. 5.7 - Prob. 26WECh. 5.7 - Prob. 27WECh. 5.7 - Prob. 28WECh. 5.7 - Prob. 29WECh. 5.7 - Prob. 30WECh. 5.7 - Prob. 31WECh. 5.7 - Prob. 32WECh. 5.7 - Prob. 33WECh. 5.7 - Prob. 34WECh. 5.7 - Prob. 35WECh. 5.7 - Prob. 36WECh. 5.7 - Prob. 37WECh. 5.7 - Prob. 38WECh. 5.7 - Prob. 39WECh. 5.7 - Prob. 40WECh. 5.7 - Prob. 41WECh. 5.7 - Prob. 42WECh. 5.7 - Prob. 43WECh. 5.7 - Prob. 44WECh. 5.7 - Prob. 45WECh. 5.7 - Prob. 46WECh. 5.7 - Prob. 47WECh. 5.7 - Prob. 48WECh. 5.7 - Prob. 49WECh. 5.7 - Prob. 50WECh. 5.7 - Prob. 51WECh. 5.7 - Prob. 52WECh. 5.7 - Prob. 53WECh. 5.7 - Prob. 54WECh. 5.7 - Prob. 55WECh. 5.7 - Prob. 56WECh. 5.7 - Prob. 1MRECh. 5.7 - Prob. 2MRECh. 5.7 - Prob. 3MRECh. 5.7 - Prob. 4MRECh. 5.7 - Prob. 5MRECh. 5.7 - Prob. 6MRECh. 5.7 - Prob. 7MRECh. 5.7 - Prob. 8MRECh. 5.7 - Prob. 9MRECh. 5.7 - Prob. 10MRECh. 5.7 - Prob. 11MRECh. 5.7 - Prob. 12MRECh. 5.8 - Prob. 1OECh. 5.8 - Prob. 2OECh. 5.8 - Prob. 3OECh. 5.8 - Prob. 4OECh. 5.8 - Prob. 5OECh. 5.8 - Prob. 6OECh. 5.8 - Prob. 7OECh. 5.8 - Prob. 8OECh. 5.8 - Prob. 9OECh. 5.8 - Prob. 10OECh. 5.8 - Prob. 11OECh. 5.8 - Prob. 12OECh. 5.8 - Prob. 13OECh. 5.8 - Prob. 14OECh. 5.8 - Prob. 15OECh. 5.8 - Prob. 16OECh. 5.8 - Prob. 17OECh. 5.8 - Prob. 18OECh. 5.8 - Prob. 19OECh. 5.8 - Prob. 1WECh. 5.8 - Prob. 2WECh. 5.8 - Prob. 3WECh. 5.8 - Prob. 4WECh. 5.8 - Prob. 5WECh. 5.8 - Prob. 6WECh. 5.8 - Prob. 7WECh. 5.8 - Prob. 8WECh. 5.8 - Prob. 9WECh. 5.8 - Prob. 10WECh. 5.8 - Prob. 11WECh. 5.8 - Prob. 12WECh. 5.8 - Prob. 13WECh. 5.8 - Prob. 14WECh. 5.8 - Prob. 15WECh. 5.8 - Prob. 16WECh. 5.8 - Prob. 17WECh. 5.8 - Prob. 18WECh. 5.8 - Prob. 19WECh. 5.8 - Prob. 20WECh. 5.8 - Prob. 21WECh. 5.8 - Prob. 22WECh. 5.8 - Prob. 23WECh. 5.8 - Prob. 24WECh. 5.8 - Prob. 25WECh. 5.8 - Prob. 26WECh. 5.8 - Prob. 27WECh. 5.8 - Prob. 28WECh. 5.8 - Prob. 29WECh. 5.8 - Prob. 30WECh. 5.8 - Prob. 31WECh. 5.8 - Prob. 32WECh. 5.8 - Prob. 33WECh. 5.8 - Prob. 34WECh. 5.8 - Prob. 35WECh. 5.8 - Prob. 36WECh. 5.8 - Prob. 37WECh. 5.8 - Prob. 38WECh. 5.8 - Prob. 39WECh. 5.8 - Prob. 40WECh. 5.8 - Prob. 41WECh. 5.8 - Prob. 42WECh. 5.8 - Prob. 43WECh. 5.8 - Prob. 44WECh. 5.8 - Prob. 45WECh. 5.8 - Prob. 46WECh. 5.8 - Prob. 47WECh. 5.8 - Prob. 48WECh. 5.8 - Prob. 49WECh. 5.8 - Prob. 50WECh. 5.8 - Prob. 51WECh. 5.8 - Prob. 52WECh. 5.8 - Prob. 53WECh. 5.8 - Prob. 54WECh. 5.8 - Prob. 55WECh. 5.8 - Prob. 56WECh. 5.8 - Prob. 1MRECh. 5.8 - Prob. 2MRECh. 5.8 - Prob. 3MRECh. 5.8 - Prob. 4MRECh. 5.8 - Prob. 5MRECh. 5.8 - Prob. 6MRECh. 5.8 - Prob. 7MRECh. 5.8 - Prob. 8MRECh. 5.8 - Prob. 9MRECh. 5.8 - Prob. 10MRECh. 5.8 - Prob. 11MRECh. 5.8 - Prob. 12MRECh. 5.8 - Prob. 13MRECh. 5.8 - Prob. 14MRECh. 5.8 - Prob. 15MRECh. 5.8 - Prob. 16MRECh. 5.8 - Prob. 17MRECh. 5.8 - Prob. 18MRECh. 5.8 - Prob. 19MRECh. 5.8 - Prob. 20MRECh. 5.8 - Prob. 21MRECh. 5.8 - Prob. 22MRECh. 5.8 - Prob. 23MRECh. 5.8 - Prob. 24MRECh. 5.8 - Prob. 25MRECh. 5.8 - Prob. 26MRECh. 5.8 - Prob. 27MRECh. 5.8 - Prob. 28MRECh. 5.8 - Prob. 29MRECh. 5.8 - Prob. 30MRECh. 5.9 - Prob. 1OECh. 5.9 - Prob. 2OECh. 5.9 - Prob. 3OECh. 5.9 - Prob. 4OECh. 5.9 - Prob. 5OECh. 5.9 - Prob. 6OECh. 5.9 - Prob. 7OECh. 5.9 - Prob. 8OECh. 5.9 - Prob. 9OECh. 5.9 - Prob. 10OECh. 5.9 - Prob. 11OECh. 5.9 - Prob. 12OECh. 5.9 - Prob. 13OECh. 5.9 - Prob. 14OECh. 5.9 - Prob. 1WECh. 5.9 - Prob. 2WECh. 5.9 - Prob. 3WECh. 5.9 - Prob. 4WECh. 5.9 - Prob. 5WECh. 5.9 - Prob. 6WECh. 5.9 - Prob. 7WECh. 5.9 - Prob. 8WECh. 5.9 - Prob. 9WECh. 5.9 - Prob. 10WECh. 5.9 - Prob. 11WECh. 5.9 - Prob. 12WECh. 5.9 - Prob. 13WECh. 5.9 - Prob. 14WECh. 5.9 - Prob. 15WECh. 5.9 - Prob. 16WECh. 5.9 - Prob. 17WECh. 5.9 - Prob. 18WECh. 5.9 - Prob. 19WECh. 5.9 - Prob. 20WECh. 5.9 - Prob. 21WECh. 5.9 - Prob. 22WECh. 5.9 - Prob. 23WECh. 5.9 - Prob. 24WECh. 5.9 - Prob. 25WECh. 5.9 - Prob. 26WECh. 5.9 - Prob. 27WECh. 5.9 - Prob. 28WECh. 5.9 - Prob. 29WECh. 5.9 - Prob. 30WECh. 5.9 - Prob. 31WECh. 5.9 - Prob. 32WECh. 5.9 - Prob. 33WECh. 5.9 - Prob. 34WECh. 5.9 - Prob. 35WECh. 5.9 - Prob. 36WECh. 5.9 - Prob. 37WECh. 5.9 - Prob. 38WECh. 5.9 - Prob. 39WECh. 5.9 - Prob. 40WECh. 5.9 - Prob. 41WECh. 5.9 - Prob. 42WECh. 5.9 - Prob. 43WECh. 5.9 - Prob. 44WECh. 5.9 - Prob. 45WECh. 5.9 - Prob. 46WECh. 5.9 - Prob. 1MRECh. 5.9 - Prob. 2MRECh. 5.9 - Prob. 3MRECh. 5.9 - Prob. 4MRECh. 5.9 - Prob. 5MRECh. 5.9 - Prob. 6MRECh. 5.9 - Prob. 7MRECh. 5.9 - Prob. 8MRECh. 5.9 - Prob. 9MRECh. 5.9 - Prob. 10MRECh. 5.9 - Prob. 11MRECh. 5.9 - Prob. 12MRECh. 5.9 - Prob. 1STCh. 5.9 - Prob. 2STCh. 5.9 - Prob. 3STCh. 5.9 - Prob. 4STCh. 5.9 - Prob. 5STCh. 5.9 - Prob. 6STCh. 5.10 - Prob. 1OECh. 5.10 - Prob. 2OECh. 5.10 - Prob. 3OECh. 5.10 - Prob. 4OECh. 5.10 - Prob. 5OECh. 5.10 - Prob. 6OECh. 5.10 - Prob. 7OECh. 5.10 - Prob. 8OECh. 5.10 - Prob. 9OECh. 5.10 - Prob. 1WECh. 5.10 - Prob. 2WECh. 5.10 - Prob. 3WECh. 5.10 - Prob. 4WECh. 5.10 - Prob. 5WECh. 5.10 - Prob. 6WECh. 5.10 - Prob. 7WECh. 5.10 - Prob. 8WECh. 5.10 - Prob. 9WECh. 5.10 - Prob. 10WECh. 5.10 - Prob. 11WECh. 5.10 - Prob. 12WECh. 5.10 - Prob. 13WECh. 5.10 - Prob. 14WECh. 5.10 - Prob. 15WECh. 5.10 - Prob. 16WECh. 5.10 - Prob. 17WECh. 5.10 - Prob. 18WECh. 5.10 - Prob. 19WECh. 5.10 - Prob. 20WECh. 5.10 - Prob. 21WECh. 5.10 - Prob. 22WECh. 5.10 - Prob. 23WECh. 5.10 - Prob. 24WECh. 5.10 - Prob. 25WECh. 5.10 - Prob. 26WECh. 5.10 - Prob. 27WECh. 5.10 - Prob. 28WECh. 5.10 - Prob. 29WECh. 5.10 - Prob. 30WECh. 5.10 - Prob. 31WECh. 5.10 - Prob. 32WECh. 5.10 - Prob. 33WECh. 5.10 - Prob. 34WECh. 5.10 - Prob. 35WECh. 5.10 - Prob. 36WECh. 5.10 - Prob. 37WECh. 5.10 - Prob. 38WECh. 5.10 - Prob. 39WECh. 5.10 - Prob. 40WECh. 5.10 - Prob. 41WECh. 5.10 - Prob. 42WECh. 5.10 - Prob. 43WECh. 5.10 - Prob. 44WECh. 5.10 - Prob. 45WECh. 5.10 - Prob. 46WECh. 5.10 - Prob. 47WECh. 5.10 - Prob. 48WECh. 5.10 - Prob. 49WECh. 5.10 - Prob. 50WECh. 5.10 - Prob. 51WECh. 5.10 - Prob. 52WECh. 5.10 - Prob. 53WECh. 5.10 - Prob. 54WECh. 5.10 - Prob. 55WECh. 5.10 - Prob. 56WECh. 5.10 - Prob. 57WECh. 5.10 - Prob. 58WECh. 5.10 - Prob. 59WECh. 5.10 - Prob. 60WECh. 5.10 - Prob. 61WECh. 5.10 - Prob. 62WECh. 5.10 - Prob. 63WECh. 5.10 - Prob. 1MRECh. 5.10 - Prob. 2MRECh. 5.10 - Prob. 3MRECh. 5.10 - Prob. 4MRECh. 5.10 - Prob. 5MRECh. 5.10 - Prob. 6MRECh. 5.10 - Prob. 7MRECh. 5.10 - Prob. 8MRECh. 5.10 - Prob. 9MRECh. 5.10 - Prob. 10MRECh. 5.10 - Prob. 11MRECh. 5.10 - Prob. 12MRECh. 5.11 - Prob. 1OECh. 5.11 - Prob. 2OECh. 5.11 - Prob. 3OECh. 5.11 - Prob. 4OECh. 5.11 - Prob. 5OECh. 5.11 - Prob. 6OECh. 5.11 - Prob. 7OECh. 5.11 - Prob. 8OECh. 5.11 - Prob. 9OECh. 5.11 - Prob. 10OECh. 5.11 - Prob. 11OECh. 5.11 - Prob. 12OECh. 5.11 - Prob. 1WECh. 5.11 - Prob. 2WECh. 5.11 - Prob. 3WECh. 5.11 - Prob. 4WECh. 5.11 - Prob. 5WECh. 5.11 - Prob. 6WECh. 5.11 - Prob. 7WECh. 5.11 - Prob. 8WECh. 5.11 - Prob. 9WECh. 5.11 - Prob. 10WECh. 5.11 - Prob. 11WECh. 5.11 - Prob. 12WECh. 5.11 - Prob. 13WECh. 5.11 - Prob. 14WECh. 5.11 - Prob. 15WECh. 5.11 - Prob. 16WECh. 5.11 - Prob. 17WECh. 5.11 - Prob. 18WECh. 5.11 - Prob. 19WECh. 5.11 - Prob. 20WECh. 5.11 - Prob. 21WECh. 5.11 - Prob. 22WECh. 5.11 - Prob. 23WECh. 5.11 - Prob. 24WECh. 5.11 - Prob. 25WECh. 5.11 - Prob. 26WECh. 5.11 - Prob. 27WECh. 5.11 - Prob. 28WECh. 5.11 - Prob. 29WECh. 5.11 - Prob. 30WECh. 5.11 - Prob. 31WECh. 5.11 - Prob. 32WECh. 5.11 - Prob. 33WECh. 5.11 - Prob. 34WECh. 5.11 - Prob. 35WECh. 5.11 - Prob. 36WECh. 5.11 - Prob. 37WECh. 5.11 - Prob. 38WECh. 5.11 - Prob. 39WECh. 5.11 - Prob. 40WECh. 5.11 - Prob. 41WECh. 5.11 - Prob. 42WECh. 5.11 - Prob. 43WECh. 5.11 - Prob. 44WECh. 5.11 - Prob. 45WECh. 5.11 - Prob. 46WECh. 5.11 - Prob. 47WECh. 5.11 - Prob. 48WECh. 5.11 - Prob. 49WECh. 5.11 - Prob. 50WECh. 5.11 - Prob. 51WECh. 5.11 - Prob. 52WECh. 5.11 - Prob. 53WECh. 5.11 - Prob. 54WECh. 5.11 - Prob. 55WECh. 5.11 - Prob. 56WECh. 5.11 - Prob. 57WECh. 5.11 - Prob. 58WECh. 5.11 - Prob. 1MRECh. 5.11 - Prob. 2MRECh. 5.11 - Prob. 3MRECh. 5.11 - Prob. 4MRECh. 5.11 - Prob. 5MRECh. 5.11 - Prob. 6MRECh. 5.11 - Prob. 7MRECh. 5.11 - Prob. 8MRECh. 5.11 - Prob. 9MRECh. 5.11 - Prob. 10MRECh. 5.11 - Prob. 11MRECh. 5.11 - Prob. 12MRECh. 5.12 - Prob. 1OECh. 5.12 - Prob. 2OECh. 5.12 - Prob. 3OECh. 5.12 - Prob. 4OECh. 5.12 - Prob. 5OECh. 5.12 - Prob. 6OECh. 5.12 - Prob. 7OECh. 5.12 - Prob. 8OECh. 5.12 - Prob. 9OECh. 5.12 - Prob. 10OECh. 5.12 - Prob. 11OECh. 5.12 - Prob. 12OECh. 5.12 - Prob. 1WECh. 5.12 - Prob. 2WECh. 5.12 - Prob. 3WECh. 5.12 - Prob. 4WECh. 5.12 - Prob. 5WECh. 5.12 - Prob. 6WECh. 5.12 - Prob. 7WECh. 5.12 - Prob. 8WECh. 5.12 - Prob. 9WECh. 5.12 - Prob. 10WECh. 5.12 - Prob. 11WECh. 5.12 - Prob. 12WECh. 5.12 - Prob. 13WECh. 5.12 - Prob. 14WECh. 5.12 - Prob. 15WECh. 5.12 - Prob. 16WECh. 5.12 - Prob. 17WECh. 5.12 - Prob. 18WECh. 5.12 - Prob. 19WECh. 5.12 - Prob. 20WECh. 5.12 - Prob. 21WECh. 5.12 - Prob. 22WECh. 5.12 - Prob. 23WECh. 5.12 - Prob. 24WECh. 5.12 - Prob. 25WECh. 5.12 - Prob. 26WECh. 5.12 - Prob. 27WECh. 5.12 - Prob. 28WECh. 5.12 - Prob. 29WECh. 5.12 - Prob. 30WECh. 5.12 - Prob. 31WECh. 5.12 - Prob. 32WECh. 5.12 - Prob. 33WECh. 5.12 - Prob. 34WECh. 5.12 - Prob. 35WECh. 5.12 - Prob. 36WECh. 5.12 - Prob. 37WECh. 5.12 - Prob. 38WECh. 5.12 - Prob. 39WECh. 5.12 - Prob. 40WECh. 5.12 - Prob. 41WECh. 5.12 - Prob. 42WECh. 5.12 - Prob. 43WECh. 5.12 - Prob. 44WECh. 5.12 - Prob. 45WECh. 5.12 - Prob. 46WECh. 5.12 - Prob. 47WECh. 5.12 - Prob. 48WECh. 5.12 - Prob. 49WECh. 5.12 - Prob. 50WECh. 5.12 - Prob. 51WECh. 5.12 - Prob. 52WECh. 5.12 - Prob. 53WECh. 5.12 - Prob. 54WECh. 5.12 - Prob. 55WECh. 5.12 - Prob. 1MRECh. 5.12 - Prob. 2MRECh. 5.12 - Prob. 3MRECh. 5.12 - Prob. 4MRECh. 5.12 - Prob. 5MRECh. 5.12 - Prob. 6MRECh. 5.12 - Prob. 7MRECh. 5.12 - Prob. 8MRECh. 5.12 - Prob. 9MRECh. 5.12 - Prob. 10MRECh. 5.12 - Prob. 11MRECh. 5.12 - Prob. 12MRECh. 5.13 - Prob. 1PCh. 5.13 - Prob. 2PCh. 5.13 - Prob. 3PCh. 5.13 - Prob. 4PCh. 5.13 - Prob. 5PCh. 5.13 - Prob. 6PCh. 5.13 - Prob. 7PCh. 5.13 - Prob. 8PCh. 5.13 - Prob. 9PCh. 5.13 - Prob. 10PCh. 5.13 - Prob. 11PCh. 5.13 - Prob. 12PCh. 5.13 - Prob. 13PCh. 5.13 - Prob. 14PCh. 5.13 - Prob. 15PCh. 5.13 - Prob. 16PCh. 5.13 - Prob. 17PCh. 5.13 - Prob. 18PCh. 5.13 - Prob. 19PCh. 5.13 - Prob. 20PCh. 5.13 - Prob. 21PCh. 5.13 - Prob. 22PCh. 5.13 - Prob. 23PCh. 5.13 - Prob. 24PCh. 5.13 - Prob. 25PCh. 5.13 - Prob. 26PCh. 5.13 - Prob. 27PCh. 5.13 - Prob. 28PCh. 5.13 - Prob. 29PCh. 5.13 - Prob. 30PCh. 5.13 - Prob. 31PCh. 5.13 - Prob. 32PCh. 5.13 - Prob. 1MRECh. 5.13 - Prob. 2MRECh. 5.13 - Prob. 3MRECh. 5.13 - Prob. 4MRECh. 5.13 - Prob. 5MRECh. 5.13 - Prob. 6MRECh. 5.13 - Prob. 7MRECh. 5.13 - Prob. 8MRECh. 5.13 - Prob. 9MRECh. 5.13 - Prob. 10MRECh. 5.13 - Prob. 11MRECh. 5.13 - Prob. 12MRECh. 5.13 - Prob. 13MRECh. 5.13 - Prob. 14MRECh. 5.13 - Prob. 15MRECh. 5.13 - Prob. 1STCh. 5.13 - Prob. 2STCh. 5.13 - Prob. 3STCh. 5.13 - Prob. 4STCh. 5.13 - Prob. 5STCh. 5.13 - Prob. 6STCh. 5.13 - Prob. 7STCh. 5.13 - Prob. 8STCh. 5.13 - Prob. 9STCh. 5.13 - Prob. 1ECh. 5.13 - Prob. 2ECh. 5.13 - Prob. 3ECh. 5.13 - Prob. 4ECh. 5.13 - Prob. 5ECh. 5.13 - Prob. 6ECh. 5.13 - Prob. 7ECh. 5 - Prob. 1CRCh. 5 - Prob. 2CRCh. 5 - Prob. 3CRCh. 5 - Prob. 4CRCh. 5 - Prob. 5CRCh. 5 - Prob. 6CRCh. 5 - Prob. 7CRCh. 5 - Prob. 8CRCh. 5 - Prob. 9CRCh. 5 - Prob. 10CRCh. 5 - Prob. 11CRCh. 5 - Prob. 12CRCh. 5 - Prob. 13CRCh. 5 - Prob. 14CRCh. 5 - Prob. 15CRCh. 5 - Prob. 16CRCh. 5 - Prob. 17CRCh. 5 - Prob. 18CRCh. 5 - Prob. 19CRCh. 5 - Prob. 20CRCh. 5 - Prob. 21CRCh. 5 - Prob. 22CRCh. 5 - Prob. 23CRCh. 5 - Prob. 24CRCh. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - Prob. 3CTCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Prob. 13CTCh. 5 - Prob. 14CTCh. 5 - Prob. 15CTCh. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - Prob. 18CTCh. 5 - Prob. 19CTCh. 5 - Prob. 20CTCh. 5 - Prob. 21CTCh. 5 - Prob. 22CTCh. 5 - Prob. 23CTCh. 5 - Prob. 24CTCh. 5 - Prob. 25CTCh. 5 - Prob. 26CTCh. 5 - Prob. 27CTCh. 5 - Prob. 28CTCh. 5 - Prob. 29CTCh. 5 - Prob. 30CTCh. 5 - Prob. 31CTCh. 5 - Prob. 32CTCh. 5 - Prob. 33CTCh. 5 - Prob. 34CTCh. 5 - Prob. 35CTCh. 5 - Prob. 36CTCh. 5 - Prob. 37CTCh. 5 - Prob. 38CTCh. 5 - Prob. 1CLRCh. 5 - Prob. 2CLRCh. 5 - Prob. 3CLRCh. 5 - Prob. 4CLRCh. 5 - Prob. 5CLRCh. 5 - Prob. 6CLRCh. 5 - Prob. 7CLRCh. 5 - Prob. 8CLRCh. 5 - Prob. 9CLRCh. 5 - Prob. 10CLRCh. 5 - Prob. 11CLRCh. 5 - Prob. 12CLRCh. 5 - Prob. 13CLRCh. 5 - Prob. 14CLRCh. 5 - Prob. 15CLRCh. 5 - Prob. 16CLRCh. 5 - Prob. 17CLRCh. 5 - Prob. 18CLRCh. 5 - Prob. 19CLRCh. 5 - Prob. 20CLRCh. 5 - Prob. 21CLRCh. 5 - Prob. 22CLRCh. 5 - Prob. 23CLRCh. 5 - Prob. 24CLRCh. 5 - Prob. 25CLRCh. 5 - Prob. 26CLRCh. 5 - Prob. 27CLRCh. 5 - Prob. 28CLRCh. 5 - Prob. 29CLRCh. 5 - Prob. 30CLRCh. 5 - Prob. 31CLRCh. 5 - Prob. 32CLRCh. 5 - Prob. 33CLRCh. 5 - Prob. 34CLRCh. 5 - Prob. 35CLRCh. 5 - Prob. 36CLRCh. 5 - Prob. 37CLRCh. 5 - Prob. 38CLRCh. 5 - Prob. 39CLRCh. 5 - Prob. 40CLRCh. 5 - Prob. 41CLRCh. 5 - Prob. 1MSCh. 5 - Prob. 2MSCh. 5 - Prob. 3MSCh. 5 - Prob. 4MSCh. 5 - Prob. 5MSCh. 5 - Prob. 1MPSCh. 5 - Prob. 2MPSCh. 5 - Prob. 3MPSCh. 5 - Prob. 4MPSCh. 5 - Prob. 5MPSCh. 5 - Prob. 6MPSCh. 5 - Prob. 7MPSCh. 5 - Prob. 8MPSCh. 5 - Prob. 9MPSCh. 5 - Prob. 10MPSCh. 5 - Prob. 11MPSCh. 5 - Prob. 12MPSCh. 5 - Prob. 13MPSCh. 5 - Prob. 14MPS

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