Problem

Factor each polynomial completely. a. $a b x^{2}+…

01:43

Question

Answered step-by-step

Problem 72 Hard Difficulty

Find the partial fraction decomposition for $\frac{8 x^{2}+17 x+12}{x^{3}+3 x^{2}+2 x}$

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Algebra

Precalculus Functions and Graphs

Chapter 9

Matrices and Determinants

Section 2

Operations with Matrices

Discussion

You must be signed in to discuss.

Top Algebra Educators

Watch More Solved Questions in Chapter 9

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Video Transcript

to find the partial fraction decomposition of this rational expression. We need to start by factoring the denominator and the denominator factors into X Times X plus one times X plus two and the numerator can stay the same. So this means that our partial fractions there will be three of them, one with the denominator x one with the denominator X plus one and one with the denominator X Plus two and the numerator CZ. For now, we'll call them A B and C on our job here is to figure out the values of A, B and C. So now we have a rational equation, and we're gonna multiply both sides of the equation by X by X plus one and by X plus two. What that does to the left side of the equation is it eliminates the denominator. And now what we have on the left is eight x squared plus 17 x plus 12 and on the right. The first fraction has X on the bottom that cancels with our X that we multiplied by and we're left with a Times X plus one times X plus two. For the second fraction, the X plus ones cancel and we're left with B times X Times X plus two. And for the third fraction, the X plus twos. Cancel and we're left with C times, X Times X plus one. We're going to use this equation to find the values of A, B and C, and the method I'm going to use is to substitute inconvenient values of X. So for the first convenient value of X, I'm going to choose X equals zero. If X equals zero, the left side of the equation is just 12 and the right side of the equation will be a times one times two. So two way plus B time zero because X will be zero plus c time. Zero. So all we have is 12 equals two a. And that tells us that is going to be six. Now I'm going to find another convenient value for X to tuck to substitute in. So I'm going to use X equals negative one because it makes this factor zero and then after that, for the third convenient value of X to plug in, I'm going to choose X equals negative, too, because it makes this factor zero. Okay, so Here we go. Substituting in X equals negative one, and that's going to give us three equals. The first part will be zero because we have the X plus one there, so that's going to be zero. The next part will be be times negative, one times one. So that's gonna be the opposite of B. And the third part will be zero, because the X plus one will be zero. So now we know that B is negative three and then lastly, we can substitute in X equals negative, too. And the left side of the equation will be 10. And this part is going to be zero. So the whole first term is hero. This part is going to be zero. So the whole second term zero and the last term is going to be C times negative two times negative one. And that's to see. So now we know that sea is five. Okay, now that we know a, B and C remember that a waas six, we substitute those back into the partial fractions, and our answer is six over X minus three over X plus one minus three. Because we had negative three for B plus five over X Plus two, and you can check that answer by adding it's attracting those fractions and see that it matches with the original problem.

Get More Help with this Textbook

Mark Dugopolski

Precalculus Functions and Graphs

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

Factor each polynomial completely. a. $a b x^{2}+…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Precalculus Functions and Graphs

Related Topics

Discussion

Top Algebra Educators

Alayna Handiak

Caleb Elmore

Maria Giefer

Kristen Karbon

Algebra Courses

Recommended Videos

Watch More Solved Questions in Chapter 9

Video Transcript

Mark Dugopolski

Precalculus Functions and Graphs

Alayna Handiak

Caleb Elmore

Maria Giefer

Kristen Karbon

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Precalculus Functions and Graphs

Alayna Handiak

Caleb Elmore

Maria Giefer

Kristen Karbon

Mark DugopolskiPrecalculus Functions and Graphs

Alayna Handiak

Caleb Elmore

Maria Giefer

Kristen Karbon

Mark Dugopolski

Precalculus Functions and Graphs