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High School Math Algebra High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

To use the rational root theorem to find all the possible rational roots of the equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 and to find all the actual rational roots if any. The possible rational roots are 1 , − 1 , 2 , − 2 , 4 , − 4 , 1 7 , − 1 7 , 2 7 , − 2 7 , 4 7 and − 4 7 . The only rational root of the equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 is 2 7 . Given: The equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 . Concept Used: Rational Root Theorem: Let p x = a n x n + a n − 1 x n − 1 + ⋅ ⋅ ⋅ a 0 be a polynomial with integer coefficients. There are a limited number of possible roots of p x = 0 : Integer roots must be factors of a 0 . Rational roots must have reduced form p q where p is an integer factor of a 0 and q is an integer factor of a n . Calculation: Suppose that p x = 7 x 3 − 2 x 2 − 14 x + 4 . Observe that the leading coefficient of p x is 7 and that the constant term of p x is 4 . Now, the leading coefficient 7 has only four factors: 1 , − 1 , 7 and − 7 . Also, the constant term 4 has only six factors: 1 , − 1 , 2 , − 2 , 4 and − 4 . Now, by the rational root theorem, the possible rational roots of p x are 1 1 , − 1 1 , 2 1 , − 2 1 , 4 1 , − 4 1 , 1 − 1 , − 1 − 1 , 2 − 1 , − 2 − 1 , 4 − 1 , − 4 − 1 , 1 7 , − 1 7 , 2 7 , − 2 7 , 4 7 , − 4 7 , 1 − 7 , − 1 − 7 , 2 − 7 , − 2 − 7 , 4 − 7 and − 4 − 7 . That is, the possible rational roots of p x are 1 , − 1 , 2 , − 2 , 4 , − 4 , 1 7 , − 1 7 , 2 7 , − 2 7 , 4 7 and − 4 7 . x 1 − 1 2 − 2 4 − 4 1 7 − 1 7 2 7 − 2 7 4 7 − 4 7 p x 7 ⋅ 1 3 − 2 ⋅ 1 2 − 14 ⋅ 1 + 4 = − 5 9 24 − 32 364 − 420 97 49 291 49 0 376 49 − 164 49 492 49 The table shows the values of the function p x for the possible roots, 1 , − 1 , 2 , − 2 , 4 , − 4 , 1 7 , − 1 7 , 2 7 , − 2 7 , 4 7 and − 4 7 : Observe that only 2 7 is an actual root of the polynomial. Thus, the only rational root of the polynomial p x = 7 x 3 − 2 x 2 − 14 x + 4 is 2 7 . That is, the only rational root of the equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 is 2 7 . Conclusion: The only rational root of the equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 is 2 7 .

To use the rational root theorem to find all the possible rational roots of the equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 and to find all the actual rational roots if any. The possible rational roots are 1 , − 1 , 2 , − 2 , 4 , − 4 , 1 7 , − 1 7 , 2 7 , − 2 7 , 4 7 and − 4 7 . The only rational root of the equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 is 2 7 . Given: The equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 . Concept Used: Rational Root Theorem: Let p x = a n x n + a n − 1 x n − 1 + ⋅ ⋅ ⋅ a 0 be a polynomial with integer coefficients. There are a limited number of possible roots of p x = 0 : Integer roots must be factors of a 0 . Rational roots must have reduced form p q where p is an integer factor of a 0 and q is an integer factor of a n . Calculation: Suppose that p x = 7 x 3 − 2 x 2 − 14 x + 4 . Observe that the leading coefficient of p x is 7 and that the constant term of p x is 4 . Now, the leading coefficient 7 has only four factors: 1 , − 1 , 7 and − 7 . Also, the constant term 4 has only six factors: 1 , − 1 , 2 , − 2 , 4 and − 4 . Now, by the rational root theorem, the possible rational roots of p x are 1 1 , − 1 1 , 2 1 , − 2 1 , 4 1 , − 4 1 , 1 − 1 , − 1 − 1 , 2 − 1 , − 2 − 1 , 4 − 1 , − 4 − 1 , 1 7 , − 1 7 , 2 7 , − 2 7 , 4 7 , − 4 7 , 1 − 7 , − 1 − 7 , 2 − 7 , − 2 − 7 , 4 − 7 and − 4 − 7 . That is, the possible rational roots of p x are 1 , − 1 , 2 , − 2 , 4 , − 4 , 1 7 , − 1 7 , 2 7 , − 2 7 , 4 7 and − 4 7 . x 1 − 1 2 − 2 4 − 4 1 7 − 1 7 2 7 − 2 7 4 7 − 4 7 p x 7 ⋅ 1 3 − 2 ⋅ 1 2 − 14 ⋅ 1 + 4 = − 5 9 24 − 32 364 − 420 97 49 291 49 0 376 49 − 164 49 492 49 The table shows the values of the function p x for the possible roots, 1 , − 1 , 2 , − 2 , 4 , − 4 , 1 7 , − 1 7 , 2 7 , − 2 7 , 4 7 and − 4 7 : Observe that only 2 7 is an actual root of the polynomial. Thus, the only rational root of the polynomial p x = 7 x 3 − 2 x 2 − 14 x + 4 is 2 7 . That is, the only rational root of the equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 is 2 7 . Conclusion: The only rational root of the equation 7 x 3 − 2 x 2 − 14 x + 4 = 0 is 2 7 .

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

15th Edition

ISBN: 9780133281163

Author: Prentice Hall

Publisher: Prentice Hall

See similar textbooks

Expert Solution & Answer

Chapter 5.5, Problem 15PPSE

Solution

To use the rational root theorem to find all the possible rational roots of the equation $7x3−2x2−14x+4=0$ and to find all the actual rational roots if any.

The possible rational roots are $1,−1,2,−2,4,−4,17,−17,27,−27,47$ and $−47$ .

The only rational root of the equation $7x3−2x2−14x+4=0$ is $27$ .

Given:

The equation $7x3−2x2−14x+4=0$ .

Concept Used:

Rational Root Theorem:

Let $px=anxn+an−1xn−1+⋅⋅⋅a0$ be a polynomial with integer coefficients. There are a limited number of possible roots of $px=0$ :

Integer roots must be factors of $a0$ .

Rational roots must have reduced form $pq$ where $p$ is an integer factor of $a0$ and $q$ is an integer factor of $an$ .

Calculation:

Suppose that $px=7x3−2x2−14x+4$ .

Observe that the leading coefficient of $px$ is $7$ and that the constant term of $px$ is $4$ .

Now, the leading coefficient $7$ has only four factors: $1,−1,7$ and $−7$ .

Also, the constant term $4$ has only six factors: $1,−1,2,−2,4$ and $−4$ .

Now, by the rational root theorem, the possible rational roots of $px$ are $11,−11,21,−21,41,−41,1−1,−1−1,2−1,−2−1,4−1,−4−1,17,−17,27,−27,47,−47,1−7,−1−7,2−7,−2−7,4−7$ and $−4−7$ .

That is, the possible rational roots of $px$ are $1,−1,2,−2,4,−4,17,−17,27,−27,47$ and $−47$ .

$x$ $1$ $−1$ $2$ $−2$ $4$ $−4$ $17$ $−17$ $27$ $−27$ $47$ $−47$
$px$ $7⋅13−2⋅12−14⋅1+4=−5$ $9$ $24$ $−32$ $364$ $−420$ $9749$ $29149$ $0$ $37649$ $−16449$ $49249$

The table shows the values of the function $px$ for the possible roots, $1,−1,2,−2,4,−4,17,−17,27,−27,47$ and $−47$ :

Observe that only $27$ is an actual root of the polynomial.

Thus, the only rational root of the polynomial $px=7x3−2x2−14x+4$ is $27$ .

That is, the only rational root of the equation $7x3−2x2−14x+4=0$ is $27$ .

Conclusion:

The only rational root of the equation $7x3−2x2−14x+4=0$ is $27$ .

Chapter 5.5, Problem 14PPSE

Chapter 5.5, Problem 16PPSE

Chapter 5 Solutions

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

Ch. 5.1 - Prob. 1LC Ch. 5.1 - Prob. 2LC Ch. 5.1 - Prob. 3LC Ch. 5.1 - Prob. 4LC Ch. 5.1 - Prob. 5LC Ch. 5.1 - Prob. 6LC Ch. 5.1 - Prob. 7LC Ch. 5.1 - Prob. 8PPSE Ch. 5.1 - Prob. 9PPSE Ch. 5.1 - Prob. 10PPSE

Ch. 5.1 - Prob. 11PPSE Ch. 5.1 - Prob. 12PPSE Ch. 5.1 - Prob. 13PPSE Ch. 5.1 - Prob. 14PPSE Ch. 5.1 - Prob. 15PPSE Ch. 5.1 - Prob. 16PPSE Ch. 5.1 - Prob. 17PPSE Ch. 5.1 - Prob. 18PPSE Ch. 5.1 - Prob. 19PPSE Ch. 5.1 - Prob. 20PPSE Ch. 5.1 - Prob. 21PPSE Ch. 5.1 - Prob. 22PPSE Ch. 5.1 - Prob. 23PPSE Ch. 5.1 - Prob. 24PPSE Ch. 5.1 - Prob. 25PPSE Ch. 5.1 - Prob. 26PPSE Ch. 5.1 - Prob. 27PPSE Ch. 5.1 - Prob. 28PPSE Ch. 5.1 - Prob. 29PPSE Ch. 5.1 - Prob. 30PPSE Ch. 5.1 - Prob. 31PPSE Ch. 5.1 - Prob. 32PPSE Ch. 5.1 - Prob. 33PPSE Ch. 5.1 - Prob. 34PPSE Ch. 5.1 - Prob. 35PPSE Ch. 5.1 - Prob. 36PPSE Ch. 5.1 - Prob. 37PPSE Ch. 5.1 - Prob. 38PPSE Ch. 5.1 - Prob. 39PPSE Ch. 5.1 - Prob. 40PPSE Ch. 5.1 - Prob. 41PPSE Ch. 5.1 - Prob. 42PPSE Ch. 5.1 - Prob. 43PPSE Ch. 5.1 - Prob. 44PPSE Ch. 5.1 - Prob. 45PPSE Ch. 5.1 - Prob. 46PPSE Ch. 5.1 - Prob. 47PPSE Ch. 5.1 - Prob. 48PPSE Ch. 5.1 - Prob. 49PPSE Ch. 5.1 - Prob. 50PPSE Ch. 5.1 - Prob. 51PPSE Ch. 5.1 - Prob. 52PPSE Ch. 5.1 - Prob. 53PPSE Ch. 5.1 - Prob. 54PPSE Ch. 5.1 - Prob. 55PPSE Ch. 5.1 - Prob. 56PPSE Ch. 5.1 - Prob. 57PPSE Ch. 5.2 - Prob. 1LC Ch. 5.2 - Prob. 2LC Ch. 5.2 - Prob. 3LC Ch. 5.2 - Prob. 4LC Ch. 5.2 - Prob. 5LC Ch. 5.2 - Prob. 6LC Ch. 5.2 - Prob. 7PPSE Ch. 5.2 - Prob. 8PPSE Ch. 5.2 - Prob. 9PPSE Ch. 5.2 - Prob. 10PPSE Ch. 5.2 - Prob. 11PPSE Ch. 5.2 - Prob. 12PPSE Ch. 5.2 - Prob. 13PPSE Ch. 5.2 - Prob. 14PPSE Ch. 5.2 - Prob. 15PPSE Ch. 5.2 - Prob. 16PPSE Ch. 5.2 - Prob. 17PPSE Ch. 5.2 - Prob. 18PPSE Ch. 5.2 - Prob. 19PPSE Ch. 5.2 - Prob. 20PPSE Ch. 5.2 - Prob. 21PPSE Ch. 5.2 - Prob. 22PPSE Ch. 5.2 - Prob. 23PPSE Ch. 5.2 - Prob. 24PPSE Ch. 5.2 - Prob. 25PPSE Ch. 5.2 - Prob. 26PPSE Ch. 5.2 - Prob. 27PPSE Ch. 5.2 - Prob. 28PPSE Ch. 5.2 - Prob. 29PPSE Ch. 5.2 - Prob. 30PPSE Ch. 5.2 - Prob. 31PPSE Ch. 5.2 - Prob. 32PPSE Ch. 5.2 - Prob. 33PPSE Ch. 5.2 - Prob. 34PPSE Ch. 5.2 - Prob. 35PPSE Ch. 5.2 - Prob. 36PPSE Ch. 5.2 - Prob. 37PPSE Ch. 5.2 - Prob. 38PPSE Ch. 5.2 - Prob. 39PPSE Ch. 5.2 - Prob. 40PPSE Ch. 5.2 - Prob. 41PPSE Ch. 5.2 - Prob. 42PPSE Ch. 5.2 - 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Prob. 5E Ch. 5.6 - Prob. 1LC Ch. 5.6 - Prob. 2LC Ch. 5.6 - Prob. 3LC Ch. 5.6 - Prob. 4LC Ch. 5.6 - Prob. 5LC Ch. 5.6 - Prob. 6LC Ch. 5.6 - Prob. 7LC Ch. 5.6 - Prob. 8PPSE Ch. 5.6 - Prob. 9PPSE Ch. 5.6 - Prob. 10PPSE Ch. 5.6 - Prob. 11PPSE Ch. 5.6 - Prob. 12PPSE Ch. 5.6 - Prob. 13PPSE Ch. 5.6 - Prob. 14PPSE Ch. 5.6 - Prob. 15PPSE Ch. 5.6 - Prob. 16PPSE Ch. 5.6 - Prob. 17PPSE Ch. 5.6 - Prob. 18PPSE Ch. 5.6 - Prob. 19PPSE Ch. 5.6 - Prob. 20PPSE Ch. 5.6 - Prob. 21PPSE Ch. 5.6 - Prob. 22PPSE Ch. 5.6 - Prob. 23PPSE Ch. 5.6 - Prob. 24PPSE Ch. 5.6 - Prob. 25PPSE Ch. 5.6 - Prob. 26PPSE Ch. 5.6 - Prob. 27PPSE Ch. 5.6 - Prob. 28PPSE Ch. 5.6 - Prob. 29PPSE Ch. 5.6 - Prob. 30PPSE Ch. 5.6 - Prob. 31PPSE Ch. 5.6 - Prob. 32PPSE Ch. 5.6 - Prob. 33PPSE Ch. 5.6 - Prob. 34PPSE Ch. 5.6 - Prob. 35PPSE Ch. 5.6 - Prob. 36PPSE Ch. 5.6 - Prob. 37PPSE Ch. 5.6 - Prob. 38PPSE Ch. 5.6 - Prob. 39PPSE Ch. 5.6 - Prob. 40PPSE Ch. 5.6 - Prob. 41PPSE Ch. 5.6 - Prob. 42PPSE Ch. 5.6 - Prob. 43PPSE Ch. 5.6 - Prob. 44PPSE Ch. 5.6 - 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Prob. 20PPSE Ch. 5.7 - Prob. 21PPSE Ch. 5.7 - Prob. 22PPSE Ch. 5.7 - Prob. 23PPSE Ch. 5.7 - Prob. 24PPSE Ch. 5.7 - Prob. 25PPSE Ch. 5.7 - Prob. 26PPSE Ch. 5.7 - Prob. 27PPSE Ch. 5.7 - Prob. 28PPSE Ch. 5.7 - Prob. 29PPSE Ch. 5.7 - Prob. 30PPSE Ch. 5.7 - Prob. 31PPSE Ch. 5.7 - Prob. 32PPSE Ch. 5.7 - Prob. 33PPSE Ch. 5.7 - Prob. 34PPSE Ch. 5.7 - Prob. 35PPSE Ch. 5.7 - Prob. 36PPSE Ch. 5.7 - Prob. 37PPSE Ch. 5.7 - Prob. 38PPSE Ch. 5.7 - Prob. 39PPSE Ch. 5.7 - Prob. 40PPSE Ch. 5.7 - Prob. 41PPSE Ch. 5.7 - Prob. 42PPSE Ch. 5.7 - Prob. 43PPSE Ch. 5.7 - Prob. 44PPSE Ch. 5.7 - Prob. 45PPSE Ch. 5.7 - Prob. 46PPSE Ch. 5.7 - Prob. 47PPSE Ch. 5.7 - Prob. 48PPSE Ch. 5.7 - Prob. 49PPSE Ch. 5.7 - Prob. 50PPSE Ch. 5.7 - Prob. 51PPSE Ch. 5.7 - Prob. 52PPSE Ch. 5.7 - Prob. 53PPSE Ch. 5.7 - Prob. 54PPSE Ch. 5.7 - Prob. 55PPSE Ch. 5.7 - Prob. 56PPSE Ch. 5.7 - Prob. 57PPSE Ch. 5.7 - Prob. 58PPSE Ch. 5.7 - Prob. 59PPSE Ch. 5.7 - Prob. 60PPSE Ch. 5.7 - Prob. 61PPSE Ch. 5.7 - Prob. 62PPSE Ch. 5.7 - Prob. 63PPSE Ch. 5.7 - Prob. 64PPSE Ch. 5.7 - Prob. 65PPSE Ch. 5.7 - Prob. 66PPSE Ch. 5.7 - Prob. 67PPSE Ch. 5.7 - Prob. 68PPSE Ch. 5.8 - Prob. 1LC Ch. 5.8 - Prob. 2LC Ch. 5.8 - Prob. 3LC Ch. 5.8 - Prob. 4LC Ch. 5.8 - Prob. 5LC Ch. 5.8 - Prob. 6LC Ch. 5.8 - Prob. 7LC Ch. 5.8 - Prob. 8PPSE Ch. 5.8 - Prob. 9PPSE Ch. 5.8 - Prob. 10PPSE Ch. 5.8 - Prob. 11PPSE Ch. 5.8 - Prob. 12PPSE Ch. 5.8 - Prob. 13PPSE Ch. 5.8 - Prob. 14PPSE Ch. 5.8 - Prob. 15PPSE Ch. 5.8 - Prob. 16PPSE Ch. 5.8 - Prob. 17PPSE Ch. 5.8 - Prob. 18PPSE Ch. 5.8 - Prob. 19PPSE Ch. 5.8 - Prob. 20PPSE Ch. 5.8 - Prob. 21PPSE Ch. 5.8 - Prob. 22PPSE Ch. 5.8 - Prob. 23PPSE Ch. 5.8 - Prob. 24PPSE Ch. 5.8 - Prob. 25PPSE Ch. 5.8 - Prob. 26PPSE Ch. 5.8 - Prob. 27PPSE Ch. 5.8 - Prob. 28PPSE Ch. 5.8 - Prob. 29PPSE Ch. 5.8 - Prob. 30PPSE Ch. 5.8 - Prob. 31PPSE Ch. 5.8 - Prob. 32PPSE Ch. 5.8 - Prob. 33PPSE Ch. 5.8 - Prob. 34PPSE Ch. 5.8 - Prob. 35PPSE Ch. 5.8 - Prob. 36PPSE Ch. 5.8 - Prob. 37PPSE Ch. 5.8 - Prob. 38PPSE Ch. 5.8 - Prob. 39PPSE Ch. 5.8 - Prob. 40PPSE Ch. 5.8 - Prob. 41PPSE Ch. 5.8 - Prob. 42PPSE Ch. 5.8 - Prob. 43PPSE Ch. 5.8 - Prob. 44PPSE Ch. 5.8 - Prob. 45PPSE Ch. 5.8 - Prob. 46PPSE Ch. 5.8 - Prob. 47PPSE Ch. 5.8 - Prob. 48PPSE Ch. 5.8 - Prob. 49PPSE Ch. 5.8 - Prob. 50PPSE Ch. 5.8 - Prob. 51PPSE Ch. 5.8 - Prob. 52PPSE Ch. 5.8 - Prob. 53PPSE Ch. 5.8 - Prob. 54PPSE Ch. 5.8 - Prob. 55PPSE Ch. 5.8 - Prob. 56PPSE Ch. 5.8 - Prob. 57PPSE Ch. 5.8 - Prob. 58PPSE Ch. 5.9 - Prob. 1LC Ch. 5.9 - Prob. 2LC Ch. 5.9 - Prob. 3LC Ch. 5.9 - Prob. 4LC Ch. 5.9 - Prob. 5LC Ch. 5.9 - Prob. 6LC Ch. 5.9 - Prob. 7PPSE Ch. 5.9 - Prob. 8PPSE Ch. 5.9 - Prob. 9PPSE Ch. 5.9 - Prob. 10PPSE Ch. 5.9 - Prob. 11PPSE Ch. 5.9 - Prob. 12PPSE Ch. 5.9 - Prob. 13PPSE Ch. 5.9 - Prob. 14PPSE Ch. 5.9 - Prob. 15PPSE Ch. 5.9 - Prob. 16PPSE Ch. 5.9 - Prob. 17PPSE Ch. 5.9 - Prob. 18PPSE Ch. 5.9 - Prob. 19PPSE Ch. 5.9 - Prob. 20PPSE Ch. 5.9 - Prob. 21PPSE Ch. 5.9 - Prob. 22PPSE Ch. 5.9 - Prob. 23PPSE Ch. 5.9 - Prob. 24PPSE Ch. 5.9 - Prob. 25PPSE Ch. 5.9 - Prob. 26PPSE Ch. 5.9 - Prob. 27PPSE Ch. 5.9 - Prob. 28PPSE Ch. 5.9 - Prob. 29PPSE Ch. 5.9 - Prob. 30PPSE Ch. 5.9 - Prob. 31PPSE Ch. 5.9 - Prob. 32PPSE Ch. 5.9 - Prob. 33PPSE Ch. 5.9 - Prob. 34PPSE Ch. 5.9 - Prob. 35PPSE Ch. 5.9 - Prob. 36PPSE Ch. 5.9 - Prob. 37PPSE Ch. 5.9 - Prob. 38PPSE Ch. 5.9 - Prob. 39PPSE Ch. 5.9 - Prob. 40PPSE Ch. 5.9 - Prob. 41PPSE Ch. 5.9 - Prob. 42PPSE Ch. 5.9 - Prob. 43PPSE Ch. 5.9 - Prob. 44PPSE Ch. 5.9 - Prob. 45PPSE Ch. 5.9 - Prob. 46PPSE Ch. 5.9 - Prob. 47PPSE Ch. 5.9 - Prob. 48PPSE Ch. 5.9 - Prob. 49PPSE Ch. 5.9 - Prob. 50PPSE Ch. 5.9 - Prob. 51PPSE Ch. 5.9 - Prob. 52PPSE Ch. 5.9 - Prob. 53PPSE Ch. 5.9 - Prob. 54PPSE Ch. 5.9 - Prob. 55PPSE Ch. 5.9 - Prob. 56PPSE Ch. 5 - Prob. 1GR Ch. 5 - Prob. 2GR Ch. 5 - Prob. 3GR Ch. 5 - Prob. 4GR Ch. 5 - Prob. 5GR Ch. 5 - Prob. 6GR Ch. 5 - Prob. 7GR Ch. 5 - Prob. 8GR Ch. 5 - Prob. 9GR Ch. 5 - Prob. 10GR Ch. 5 - Prob. 11GR Ch. 5 - Prob. 12GR Ch. 5 - Prob. 13GR Ch. 5 - Prob. 14GR Ch. 5 - Prob. 15GR Ch. 5 - Prob. 16GR Ch. 5 - Prob. 17GR Ch. 5 - Prob. 18GR Ch. 5 - Prob. 1MCQ Ch. 5 - Prob. 2MCQ Ch. 5 - Prob. 3MCQ Ch. 5 - Prob. 4MCQ Ch. 5 - Prob. 5MCQ Ch. 5 - Prob. 6MCQ Ch. 5 - Prob. 7MCQ Ch. 5 - Prob. 8MCQ Ch. 5 - Prob. 9MCQ Ch. 5 - Prob. 10MCQ Ch. 5 - Prob. 11MCQ Ch. 5 - Prob. 12MCQ Ch. 5 - Prob. 13MCQ Ch. 5 - Prob. 14MCQ Ch. 5 - Prob. 15MCQ Ch. 5 - Prob. 16MCQ Ch. 5 - Prob. 17MCQ Ch. 5 - Prob. 18MCQ Ch. 5 - Prob. 19MCQ Ch. 5 - Prob. 1CV Ch. 5 - Prob. 2CV Ch. 5 - Prob. 3CV Ch. 5 - Prob. 4CV Ch. 5 - Prob. 5E Ch. 5 - Prob. 6E Ch. 5 - Prob. 7E Ch. 5 - Prob. 8E Ch. 5 - Prob. 9E Ch. 5 - Prob. 10E Ch. 5 - Prob. 11E Ch. 5 - Prob. 12E Ch. 5 - Prob. 13E Ch. 5 - Prob. 14E Ch. 5 - Prob. 15E Ch. 5 - Prob. 16E Ch. 5 - Prob. 17E Ch. 5 - Prob. 18E Ch. 5 - Prob. 19E Ch. 5 - Prob. 20E Ch. 5 - Prob. 21E Ch. 5 - Prob. 22E Ch. 5 - Prob. 23E Ch. 5 - Prob. 24E Ch. 5 - Prob. 25E Ch. 5 - Prob. 26E Ch. 5 - Prob. 27E Ch. 5 - Prob. 28E Ch. 5 - Prob. 29E Ch. 5 - Prob. 30E Ch. 5 - Prob. 31E Ch. 5 - Prob. 32E Ch. 5 - Prob. 33E Ch. 5 - Prob. 34E Ch. 5 - Prob. 35E Ch. 5 - Prob. 36E Ch. 5 - Prob. 37E Ch. 5 - Prob. 38E Ch. 5 - Prob. 39E Ch. 5 - Prob. 40E Ch. 5 - Prob. 41E Ch. 5 - Prob. 42E Ch. 5 - Prob. 43E Ch. 5 - Prob. 44E Ch. 5 - Prob. 45E Ch. 5 - Prob. 46E Ch. 5 - Prob. 47E Ch. 5 - Prob. 48E Ch. 5 - Prob. 49E Ch. 5 - Prob. 50E Ch. 5 - Prob. 51E Ch. 5 - Prob. 52E Ch. 5 - Prob. 53E Ch. 5 - Prob. 54E Ch. 5 - Prob. 55E Ch. 5 - Prob. 56E Ch. 5 - Prob. 57E Ch. 5 - Prob. 58E Ch. 5 - Prob. 59E Ch. 5 - Prob. 60E Ch. 5 - Prob. 61E Ch. 5 - Prob. 62E Ch. 5 - Prob. 63E Ch. 5 - Prob. 64E Ch. 5 - Prob. 65E Ch. 5 - Prob. 66E Ch. 5 - Prob. 67E Ch. 5 - Prob. 68E Ch. 5 - Prob. 69E Ch. 5 - Prob. 70E Ch. 5 - Prob. 71E Ch. 5 - Prob. 72E Ch. 5 - Prob. 73E Ch. 5 - Prob. 74E Ch. 5 - Prob. 75E Ch. 5 - Prob. 76E Ch. 5 - Prob. 77E Ch. 5 - Prob. 78E Ch. 5 - Prob. 79E Ch. 5 - Prob. 80E Ch. 5 - Prob. 81E Ch. 5 - Prob. 82E Ch. 5 - Prob. 83E Ch. 5 - Prob. 84E Ch. 5 - Prob. 85E Ch. 5 - Prob. 86E Ch. 5 - Prob. 87E Ch. 5 - Prob. 88E Ch. 5 - Prob. 1CT Ch. 5 - Prob. 2CT Ch. 5 - Prob. 3CT Ch. 5 - Prob. 4CT Ch. 5 - Prob. 5CT Ch. 5 - Prob. 6CT Ch. 5 - Prob. 7CT Ch. 5 - Prob. 8CT Ch. 5 - Prob. 9CT Ch. 5 - Prob. 10CT Ch. 5 - Prob. 11CT Ch. 5 - Prob. 12CT Ch. 5 - Prob. 13CT Ch. 5 - Prob. 14CT Ch. 5 - Prob. 15CT Ch. 5 - Prob. 16CT Ch. 5 - Prob. 17CT Ch. 5 - Prob. 18CT Ch. 5 - Prob. 19CT Ch. 5 - Prob. 20CT Ch. 5 - Prob. 21CT Ch. 5 - Prob. 22CT Ch. 5 - Prob. 23CT Ch. 5 - Prob. 1CCSR Ch. 5 - Prob. 2CCSR Ch. 5 - Prob. 3CCSR Ch. 5 - Prob. 4CCSR Ch. 5 - Prob. 5CCSR Ch. 5 - Prob. 6CCSR Ch. 5 - Prob. 7CCSR Ch. 5 - Prob. 8CCSR Ch. 5 - Prob. 9CCSR Ch. 5 - Prob. 10CCSR Ch. 5 - Prob. 11CCSR Ch. 5 - Prob. 12CCSR Ch. 5 - Prob. 13CCSR Ch. 5 - Prob. 14CCSR Ch. 5 - Prob. 15CCSR Ch. 5 - Prob. 16CCSR Ch. 5 - Prob. 17CCSR Ch. 5 - Prob. 18CCSR Ch. 5 - Prob. 19CCSR Ch. 5 - Prob. 20CCSR Ch. 5 - Prob. 21CCSR Ch. 5 - Prob. 22CCSR Ch. 5 - Prob. 23CCSR

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