SOLUTION: x^2+5x-14 divided by x^3+10x+21X
Hi, I just wante to make sure I have the right answers, which is X-2 over x(X+3). Thank You!
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-> SOLUTION: x^2+5x-14 divided by x^3+10x+21X
Hi, I just wante to make sure I have the right answers, which is X-2 over x(X+3). Thank You!
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Question 78008: x^2+5x-14 divided by x^3+10x+21X
Hi, I just wante to make sure I have the right answers, which is X-2 over x(X+3). Thank You! Found 2 solutions by scott8148, jim_thompson5910:Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website! Does your problem look like this?
If this is the case, I'm afraid you don't have the answer (despite what the other tutor said. He must have quickly glanced at it).
First factor the numerator
In order to factor , first we need to ask ourselves: What two numbers multiply to -14 and add to 5? Lets find out by listing all of the possible factors of -14
Factors:
1,2,7,14,
-1,-2,-7,-14,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -14.
(-1)*(14)=-14
(-2)*(7)=-14
Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5
First Number
|
Second Number
|
Sum
1
|
-14
|
|
1+(-14)=-13
2
|
-7
|
|
2+(-7)=-5
-1
|
14
|
|
(-1)+14=13
-2
|
7
|
|
(-2)+7=5
We can see from the table that -2 and 7 add to 5.So the two numbers that multiply to -14 and add to 5 are: -2 and 7
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
substitute a=-2 and b=7
So the equation becomes:
(x-2)(x+7)
Notice that if we foil (x-2)(x+7) we get the quadratic again
In order to factor , first we need to ask ourselves: What two numbers multiply to 21 and add to 10? Lets find out by listing all of the possible factors of 21
Factors:
1,3,7,21,
-1,-3,-7,-21,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 21.
1*21=21
3*7=21
(-1)*(-21)=21
(-3)*(-7)=21
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 10
First Number
|
Second Number
|
Sum
1
|
21
|
|
1+21=22
3
|
7
|
|
3+7=10
-1
|
-21
|
|
-1+(-21)=-22
-3
|
-7
|
|
-3+(-7)=-10
We can see from the table that 3 and 7 add to 10. So the two numbers that multiply to 21 and add to 10 are: 3 and 7
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
substitute a=3 and b=7
So the equation becomes:
(x+3)(x+7)
Notice that if we foil (x+3)(x+7) we get the quadratic again
So when we factor the numerator and denominator we get:
Cancel like terms
So this is your answer.
In other words, reduces to
note: you were close though. You just had an extra x in your denominator.
Notice if you graph you get
graph of
it should be the same as the graph of graph of
We can see that they are equal. So this verifies our answer.
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