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
Expert Solution & Answer
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Chapter 5, Problem 47E
Solution

To calculate : Therational root of the given function.

The given polynomial function has four rational roots and are given by x=1,1,2 and 23 .

Given information :

The function is P(x)=3x4+2x39x2+4 .

Formula Used:

Rational Root Theorem: For a given polynomial with integer coefficients, the rational roots will be in form of pq , where p is the integer factor of the constant term and q is the integer factor of the leading coefficient.

Calculation :

Given polynomial function: P(x)=3x4+2x39x2+4 .

Find the possible rational roots.

Determine the integer factor of the constant term 4 .

  p=±1,±2 and ±4

Find the integer factor of the leading coefficient 3 .

  q=±1 and ±3

Determine the list of rational roots that will be in reduced form of (pq) .

  (pq)=±1,±2,±4,±23 and±43

Apply the synthetic division method to test the roots.

  {1    3     2   9     0      4              3       5   4  4      3     5    4   4    0¯},{1    3      2   9     0      4               3      1      8  4         3   1    8     8    4¯}

Here, the rational root is given by x=1 .

Solving further,

  {2    3     2   9     0      4               6     16    14    28       3      8      7     14    32¯},{2    3      2   9     0      4               6      8      2  4         3    4    1     2    0¯}

Here, the rational root is given by x=2 .

Solving further,

  {4    3     2    9      0         4               12     56    188    752        3     14     47     188    756¯},{4    3      2      9        0         4               12     40    124    496         3    10     31     124    500¯}

Here, the remainders are not equal to zero, so x±4 .

Solving further,

  {23    3     2    9        0            4               2       83    389    7627       3     4    193   389     3227¯},{23    3      2     9      0      4               2        0       6  4          3      0     9      6     0¯}

Here, the rational root is given by x=23 .

Solving further,

  {43    3     2    9      0         4               4       8    43    169       3     6    1     43     209¯},{43    3      2      9        0           4                4       83       769   30427          3    2    193     769    19627¯}

Here, the remainders are not equal to zero, so x±43 .

Find the product of the factors (x+2) and (x+3) .

  (x+2)(3x+2)=x(3x+2)+2(3x+2)                       =(3x2+2x)+(6x+4)                       =3x2+8x+4

Apply long division method to divide the polynomial P(x)=3x4+2x39x2+4 by 3x2+8x+4 as shown below:

  3x2+8x+4x22x+13x4+2x39x2+43x4+8x3+4x2      6x313x2+4      6x316x28x                    3x28x+4                    3x28x+4                                     0¯¯¯

Now,

  x22x+1=0(x1)2=0x=1,1

So, the other two rational roots are x=1, 1 .

Hence, the given polynomial function has four rational roots and are given by x=1,1,2 and 23 .

Chapter 5 Solutions

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

Ch. 5.1 - Prob. 11PPSECh. 5.1 - Prob. 12PPSECh. 5.1 - Prob. 13PPSECh. 5.1 - Prob. 14PPSECh. 5.1 - Prob. 15PPSECh. 5.1 - Prob. 16PPSECh. 5.1 - Prob. 17PPSECh. 5.1 - Prob. 18PPSECh. 5.1 - Prob. 19PPSECh. 5.1 - Prob. 20PPSECh. 5.1 - Prob. 21PPSECh. 5.1 - Prob. 22PPSECh. 5.1 - Prob. 23PPSECh. 5.1 - Prob. 24PPSECh. 5.1 - Prob. 25PPSECh. 5.1 - Prob. 26PPSECh. 5.1 - Prob. 27PPSECh. 5.1 - Prob. 28PPSECh. 5.1 - Prob. 29PPSECh. 5.1 - Prob. 30PPSECh. 5.1 - Prob. 31PPSECh. 5.1 - Prob. 32PPSECh. 5.1 - Prob. 33PPSECh. 5.1 - Prob. 34PPSECh. 5.1 - Prob. 35PPSECh. 5.1 - Prob. 36PPSECh. 5.1 - Prob. 37PPSECh. 5.1 - Prob. 38PPSECh. 5.1 - Prob. 39PPSECh. 5.1 - Prob. 40PPSECh. 5.1 - Prob. 41PPSECh. 5.1 - Prob. 42PPSECh. 5.1 - Prob. 43PPSECh. 5.1 - Prob. 44PPSECh. 5.1 - Prob. 45PPSECh. 5.1 - Prob. 46PPSECh. 5.1 - Prob. 47PPSECh. 5.1 - Prob. 48PPSECh. 5.1 - Prob. 49PPSECh. 5.1 - Prob. 50PPSECh. 5.1 - Prob. 51PPSECh. 5.1 - Prob. 52PPSECh. 5.1 - Prob. 53PPSECh. 5.1 - Prob. 54PPSECh. 5.1 - Prob. 55PPSECh. 5.1 - Prob. 56PPSECh. 5.1 - Prob. 57PPSECh. 5.2 - Prob. 1LCCh. 5.2 - Prob. 2LCCh. 5.2 - Prob. 3LCCh. 5.2 - Prob. 4LCCh. 5.2 - Prob. 5LCCh. 5.2 - Prob. 6LCCh. 5.2 - Prob. 7PPSECh. 5.2 - Prob. 8PPSECh. 5.2 - Prob. 9PPSECh. 5.2 - Prob. 10PPSECh. 5.2 - Prob. 11PPSECh. 5.2 - Prob. 12PPSECh. 5.2 - Prob. 13PPSECh. 5.2 - Prob. 14PPSECh. 5.2 - Prob. 15PPSECh. 5.2 - Prob. 16PPSECh. 5.2 - Prob. 17PPSECh. 5.2 - Prob. 18PPSECh. 5.2 - Prob. 19PPSECh. 5.2 - Prob. 20PPSECh. 5.2 - Prob. 21PPSECh. 5.2 - Prob. 22PPSECh. 5.2 - Prob. 23PPSECh. 5.2 - Prob. 24PPSECh. 5.2 - Prob. 25PPSECh. 5.2 - Prob. 26PPSECh. 5.2 - Prob. 27PPSECh. 5.2 - Prob. 28PPSECh. 5.2 - Prob. 29PPSECh. 5.2 - Prob. 30PPSECh. 5.2 - Prob. 31PPSECh. 5.2 - Prob. 32PPSECh. 5.2 - Prob. 33PPSECh. 5.2 - Prob. 34PPSECh. 5.2 - Prob. 35PPSECh. 5.2 - Prob. 36PPSECh. 5.2 - Prob. 37PPSECh. 5.2 - Prob. 38PPSECh. 5.2 - Prob. 39PPSECh. 5.2 - Prob. 40PPSECh. 5.2 - Prob. 41PPSECh. 5.2 - Prob. 42PPSECh. 5.2 - Prob. 43PPSECh. 5.2 - Prob. 44PPSECh. 5.2 - Prob. 45PPSECh. 5.2 - 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Prob. 20PPSECh. 5.5 - Prob. 21PPSECh. 5.5 - Prob. 22PPSECh. 5.5 - Prob. 23PPSECh. 5.5 - Prob. 24PPSECh. 5.5 - Prob. 25PPSECh. 5.5 - Prob. 26PPSECh. 5.5 - Prob. 27PPSECh. 5.5 - Prob. 28PPSECh. 5.5 - Prob. 29PPSECh. 5.5 - Prob. 30PPSECh. 5.5 - Prob. 31PPSECh. 5.5 - Prob. 32PPSECh. 5.5 - Prob. 33PPSECh. 5.5 - Prob. 34PPSECh. 5.5 - Prob. 35PPSECh. 5.5 - Prob. 36PPSECh. 5.5 - Prob. 37PPSECh. 5.5 - Prob. 38PPSECh. 5.5 - Prob. 39PPSECh. 5.5 - Prob. 40PPSECh. 5.5 - Prob. 41PPSECh. 5.5 - Prob. 42PPSECh. 5.5 - Prob. 43PPSECh. 5.5 - Prob. 44PPSECh. 5.5 - Prob. 45PPSECh. 5.5 - Prob. 46PPSECh. 5.5 - Prob. 47PPSECh. 5.5 - Prob. 48PPSECh. 5.5 - Prob. 49PPSECh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.6 - Prob. 1LCCh. 5.6 - Prob. 2LCCh. 5.6 - Prob. 3LCCh. 5.6 - Prob. 4LCCh. 5.6 - Prob. 5LCCh. 5.6 - Prob. 6LCCh. 5.6 - Prob. 7LCCh. 5.6 - Prob. 8PPSECh. 5.6 - Prob. 9PPSECh. 5.6 - Prob. 10PPSECh. 5.6 - Prob. 11PPSECh. 5.6 - Prob. 12PPSECh. 5.6 - Prob. 13PPSECh. 5.6 - Prob. 14PPSECh. 5.6 - Prob. 15PPSECh. 5.6 - Prob. 16PPSECh. 5.6 - Prob. 17PPSECh. 5.6 - Prob. 18PPSECh. 5.6 - Prob. 19PPSECh. 5.6 - Prob. 20PPSECh. 5.6 - Prob. 21PPSECh. 5.6 - Prob. 22PPSECh. 5.6 - Prob. 23PPSECh. 5.6 - Prob. 24PPSECh. 5.6 - Prob. 25PPSECh. 5.6 - Prob. 26PPSECh. 5.6 - Prob. 27PPSECh. 5.6 - Prob. 28PPSECh. 5.6 - Prob. 29PPSECh. 5.6 - Prob. 30PPSECh. 5.6 - Prob. 31PPSECh. 5.6 - Prob. 32PPSECh. 5.6 - Prob. 33PPSECh. 5.6 - Prob. 34PPSECh. 5.6 - Prob. 35PPSECh. 5.6 - Prob. 36PPSECh. 5.6 - Prob. 37PPSECh. 5.6 - Prob. 38PPSECh. 5.6 - Prob. 39PPSECh. 5.6 - Prob. 40PPSECh. 5.6 - Prob. 41PPSECh. 5.6 - Prob. 42PPSECh. 5.6 - Prob. 43PPSECh. 5.6 - Prob. 44PPSECh. 5.6 - Prob. 45PPSECh. 5.6 - Prob. 46PPSECh. 5.6 - Prob. 47PPSECh. 5.6 - Prob. 48PPSECh. 5.6 - Prob. 49PPSECh. 5.6 - Prob. 50PPSECh. 5.6 - Prob. 51PPSECh. 5.6 - Prob. 52PPSECh. 5.6 - Prob. 53PPSECh. 5.6 - Prob. 54PPSECh. 5.6 - Prob. 55PPSECh. 5.6 - Prob. 56PPSECh. 5.6 - Prob. 57PPSECh. 5.6 - Prob. 58PPSECh. 5.6 - Prob. 59PPSECh. 5.6 - Prob. 60PPSECh. 5.6 - Prob. 61PPSECh. 5.6 - Prob. 62PPSECh. 5.6 - Prob. 63PPSECh. 5.6 - Prob. 64PPSECh. 5.6 - Prob. 65PPSECh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.7 - Prob. 1LCCh. 5.7 - Prob. 2LCCh. 5.7 - Prob. 3LCCh. 5.7 - Prob. 4LCCh. 5.7 - Prob. 5LCCh. 5.7 - Prob. 6LCCh. 5.7 - Prob. 7LCCh. 5.7 - Prob. 8PPSECh. 5.7 - Prob. 9PPSECh. 5.7 - Prob. 10PPSECh. 5.7 - Prob. 11PPSECh. 5.7 - Prob. 12PPSECh. 5.7 - Prob. 13PPSECh. 5.7 - Prob. 14PPSECh. 5.7 - Prob. 15PPSECh. 5.7 - Prob. 16PPSECh. 5.7 - Prob. 17PPSECh. 5.7 - Prob. 18PPSECh. 5.7 - Prob. 19PPSECh. 5.7 - Prob. 20PPSECh. 5.7 - Prob. 21PPSECh. 5.7 - Prob. 22PPSECh. 5.7 - Prob. 23PPSECh. 5.7 - Prob. 24PPSECh. 5.7 - Prob. 25PPSECh. 5.7 - Prob. 26PPSECh. 5.7 - Prob. 27PPSECh. 5.7 - Prob. 28PPSECh. 5.7 - Prob. 29PPSECh. 5.7 - Prob. 30PPSECh. 5.7 - Prob. 31PPSECh. 5.7 - Prob. 32PPSECh. 5.7 - Prob. 33PPSECh. 5.7 - Prob. 34PPSECh. 5.7 - Prob. 35PPSECh. 5.7 - Prob. 36PPSECh. 5.7 - 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Prob. 4LCCh. 5.9 - Prob. 5LCCh. 5.9 - Prob. 6LCCh. 5.9 - Prob. 7PPSECh. 5.9 - Prob. 8PPSECh. 5.9 - Prob. 9PPSECh. 5.9 - Prob. 10PPSECh. 5.9 - Prob. 11PPSECh. 5.9 - Prob. 12PPSECh. 5.9 - Prob. 13PPSECh. 5.9 - Prob. 14PPSECh. 5.9 - Prob. 15PPSECh. 5.9 - Prob. 16PPSECh. 5.9 - Prob. 17PPSECh. 5.9 - Prob. 18PPSECh. 5.9 - Prob. 19PPSECh. 5.9 - Prob. 20PPSECh. 5.9 - Prob. 21PPSECh. 5.9 - Prob. 22PPSECh. 5.9 - Prob. 23PPSECh. 5.9 - Prob. 24PPSECh. 5.9 - Prob. 25PPSECh. 5.9 - Prob. 26PPSECh. 5.9 - Prob. 27PPSECh. 5.9 - Prob. 28PPSECh. 5.9 - Prob. 29PPSECh. 5.9 - Prob. 30PPSECh. 5.9 - Prob. 31PPSECh. 5.9 - Prob. 32PPSECh. 5.9 - Prob. 33PPSECh. 5.9 - Prob. 34PPSECh. 5.9 - Prob. 35PPSECh. 5.9 - Prob. 36PPSECh. 5.9 - Prob. 37PPSECh. 5.9 - Prob. 38PPSECh. 5.9 - Prob. 39PPSECh. 5.9 - Prob. 40PPSECh. 5.9 - Prob. 41PPSECh. 5.9 - Prob. 42PPSECh. 5.9 - Prob. 43PPSECh. 5.9 - Prob. 44PPSECh. 5.9 - Prob. 45PPSECh. 5.9 - Prob. 46PPSECh. 5.9 - Prob. 47PPSECh. 5.9 - Prob. 48PPSECh. 5.9 - Prob. 49PPSECh. 5.9 - Prob. 50PPSECh. 5.9 - Prob. 51PPSECh. 5.9 - Prob. 52PPSECh. 5.9 - Prob. 53PPSECh. 5.9 - Prob. 54PPSECh. 5.9 - Prob. 55PPSECh. 5.9 - Prob. 56PPSECh. 5 - Prob. 1GRCh. 5 - Prob. 2GRCh. 5 - Prob. 3GRCh. 5 - Prob. 4GRCh. 5 - Prob. 5GRCh. 5 - Prob. 6GRCh. 5 - Prob. 7GRCh. 5 - Prob. 8GRCh. 5 - Prob. 9GRCh. 5 - Prob. 10GRCh. 5 - Prob. 11GRCh. 5 - Prob. 12GRCh. 5 - Prob. 13GRCh. 5 - Prob. 14GRCh. 5 - Prob. 15GRCh. 5 - Prob. 16GRCh. 5 - Prob. 17GRCh. 5 - Prob. 18GRCh. 5 - Prob. 1MCQCh. 5 - Prob. 2MCQCh. 5 - Prob. 3MCQCh. 5 - Prob. 4MCQCh. 5 - Prob. 5MCQCh. 5 - Prob. 6MCQCh. 5 - Prob. 7MCQCh. 5 - Prob. 8MCQCh. 5 - Prob. 9MCQCh. 5 - Prob. 10MCQCh. 5 - Prob. 11MCQCh. 5 - Prob. 12MCQCh. 5 - Prob. 13MCQCh. 5 - Prob. 14MCQCh. 5 - Prob. 15MCQCh. 5 - Prob. 16MCQCh. 5 - Prob. 17MCQCh. 5 - Prob. 18MCQCh. 5 - Prob. 19MCQCh. 5 - Prob. 1CVCh. 5 - Prob. 2CVCh. 5 - Prob. 3CVCh. 5 - Prob. 4CVCh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - Prob. 7ECh. 5 - Prob. 8ECh. 5 - Prob. 9ECh. 5 - Prob. 10ECh. 5 - Prob. 11ECh. 5 - Prob. 12ECh. 5 - Prob. 13ECh. 5 - Prob. 14ECh. 5 - Prob. 15ECh. 5 - Prob. 16ECh. 5 - Prob. 17ECh. 5 - Prob. 18ECh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Prob. 43ECh. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - Prob. 72ECh. 5 - Prob. 73ECh. 5 - Prob. 74ECh. 5 - Prob. 75ECh. 5 - Prob. 76ECh. 5 - Prob. 77ECh. 5 - Prob. 78ECh. 5 - Prob. 79ECh. 5 - Prob. 80ECh. 5 - Prob. 81ECh. 5 - Prob. 82ECh. 5 - Prob. 83ECh. 5 - Prob. 84ECh. 5 - Prob. 85ECh. 5 - Prob. 86ECh. 5 - Prob. 87ECh. 5 - Prob. 88ECh. 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. 1CCSRCh. 5 - Prob. 2CCSRCh. 5 - Prob. 3CCSRCh. 5 - Prob. 4CCSRCh. 5 - Prob. 5CCSRCh. 5 - Prob. 6CCSRCh. 5 - Prob. 7CCSRCh. 5 - Prob. 8CCSRCh. 5 - Prob. 9CCSRCh. 5 - Prob. 10CCSRCh. 5 - Prob. 11CCSRCh. 5 - Prob. 12CCSRCh. 5 - Prob. 13CCSRCh. 5 - Prob. 14CCSRCh. 5 - Prob. 15CCSRCh. 5 - Prob. 16CCSRCh. 5 - Prob. 17CCSRCh. 5 - Prob. 18CCSRCh. 5 - Prob. 19CCSRCh. 5 - Prob. 20CCSRCh. 5 - Prob. 21CCSRCh. 5 - Prob. 22CCSRCh. 5 - Prob. 23CCSR
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