SOLUTION: Please help. I am confusing myself more every time I try to work this. Factor the following expression completely: 12y5 – 34xy4 + 14x2y3 Also, if you could please tell me

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help. I am confusing myself more every time I try to work this. Factor the following expression completely: 12y5 – 34xy4 + 14x2y3 Also, if you could please tell me       Log On


   

Question 601695: Please help. I am confusing myself more every time I try to work this.
Factor the following expression completely:
12y5 – 34xy4 + 14x2y3
Also, if you could please tell me if I answered this right I would appreciate it.
Question: Andrew factored the expression 24x^3 – 8x^2 – 32x as 8x(3x^3 – x^2 -4x) . But when Melissa applied the distributive law and multiplied out 8x(3x^3 – x^2 – 4x), she got 24x^4 – 8x^3 – 32x; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.
Answer:Since Andrew stared his factoring with 8x he should have reduced the quotent inside the parenthesis by 1. Also Melissa should have gotten 24x^4 - 8x^3 - 34x^2. The correct answer should have been 8(3x^3 - x^2 = 4x) this would have checked to the beginning expression.
Thank you in advance!
Found 3 solutions by jim_thompson5910, Edwin McCravy, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

12y%5E5-34xy%5E4%2B14x%5E2y%5E3 Start with the given expression.


2y%5E3%286y%5E2-17xy%2B7x%5E2%29 Factor out the GCF 2y%5E3.


Now let's try to factor the inner expression 6y%5E2-17xy%2B7x%5E2


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Looking at the expression 6y%5E2-17xy%2B7x%5E2, we can see that the first coefficient is 6, the second coefficient is -17, and the last coefficient is 7.


Now multiply the first coefficient 6 by the last coefficient 7 to get %286%29%287%29=42.


Now the question is: what two whole numbers multiply to 42 (the previous product) and add to the second coefficient -17?


To find these two numbers, we need to list all of the factors of 42 (the previous product).


Factors of 42:
1,2,3,6,7,14,21,42
-1,-2,-3,-6,-7,-14,-21,-42


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to 42.
1*42 = 42
2*21 = 42
3*14 = 42
6*7 = 42
(-1)*(-42) = 42
(-2)*(-21) = 42
(-3)*(-14) = 42
(-6)*(-7) = 42

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -17:


First NumberSecond NumberSum
1421+42=43
2212+21=23
3143+14=17
676+7=13
-1-42-1+(-42)=-43
-2-21-2+(-21)=-23
-3-14-3+(-14)=-17
-6-7-6+(-7)=-13



From the table, we can see that the two numbers -3 and -14 add to -17 (the middle coefficient).


So the two numbers -3 and -14 both multiply to 42 and add to -17


Now replace the middle term -17xy with -3xy-14xy. Remember, -3 and -14 add to -17. So this shows us that -3xy-14xy=-17xy.


6y%5E2%2Bhighlight%28-3xy-14xy%29%2B7x%5E2 Replace the second term -17xy with -3xy-14xy.


%286y%5E2-3xy%29%2B%28-14xy%2B7x%5E2%29 Group the terms into two pairs.


3y%282y-x%29%2B%28-14xy%2B7x%5E2%29 Factor out the GCF 3y from the first group.


3y%282y-x%29-7x%282y-x%29 Factor out -7x from the second group.


%283y-7x%29%282y-x%29 Factor out 2y-x from the entire expression.

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So 6y%5E2-17xy%2B7x%5E2 factors to %283y-7x%29%282y-x%29


which means that 2y%5E3%286y%5E2-17xy%2B7x%5E2%29 factors to 2y%5E3%283y-7x%29%282y-x%29


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Answer:


12y%5E5-34xy%5E4%2B14x%5E2y%5E3 completely factors to 2y%5E3%283y-7x%29%282y-x%29

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# 2

Andrew forgot to factor out an x from each term as well. He should have gotten

8x%283x%5E2-x-4%29

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:   

12y5 – 34xy4 + 14x2y3

Factor out 2y3

2y3(6y2 - 17xy + 7x2)

2y3(3y - 7x)(2x - y)

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Factor:

24x3 – 8x2 – 32x

8x(3x2 - x - 4)

8x(3x - 4)(x + 1)

Edwin

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Please help. I am confusing myself more every time I try to work this.
Factor the following expression completely:
12y5 – 34xy4 + 14x2y3
----
GCF: 2y^3
Factored form:
(2y^3)(6y^2 - 17xy + 7x^2)
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Also, if you could please tell me if I answered this right I would appreciate it.
Question: Andrew factored the expression
24x^3 – 8x^2 – 32x as 8x(3x^3 – x^2 -4x) .
But when Melissa applied the distributive law and multiplied out 8x(3x^3 – x^2 – 4x), she got 24x^4 – 8x^3 – 32x;
thus, Andrew’s solution does not appear to check. Why is that?
Andrew's answer should be: 8x(3x^2-x-4)
Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.
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Answer:Since Andrew stared his factoring with 8x he should have reduced the quotent inside the parenthesis by 1. Also Melissa should have gotten 24x^4 - 8x^3 - 34x^2. The correct answer should have been 8(3x^3 - x^2 = 4x) this would have checked to the beginning expression.
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True, but you still have a common factor of "x" in your answer.
The correct answer is 8x(3x^2-x-4)
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Cheers,
Stan H.
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