SOLUTION: factor completely. If polynomial is prime state this 28x^2+38x-6

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Question 621898: factor completely. If polynomial is prime state this
28x^2+38x-6
Found 2 solutions by jim_thompson5910, lenny460:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

28x%5E2%2B38x-6 Start with the given expression.


2%2814x%5E2%2B19x-3%29 Factor out the GCF 2.


Now let's try to factor the inner expression 14x%5E2%2B19x-3


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Looking at the expression 14x%5E2%2B19x-3, we can see that the first coefficient is 14, the second coefficient is 19, and the last term is -3.


Now multiply the first coefficient 14 by the last term -3 to get %2814%29%28-3%29=-42.


Now the question is: what two whole numbers multiply to -42 (the previous product) and add to the second coefficient 19?


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 19:


First NumberSecond NumberSum
1-421+(-42)=-41
2-212+(-21)=-19
3-143+(-14)=-11
6-76+(-7)=-1
-142-1+42=41
-221-2+21=19
-314-3+14=11
-67-6+7=1



From the table, we can see that the two numbers -2 and 21 add to 19 (the middle coefficient).


So the two numbers -2 and 21 both multiply to -42 and add to 19


Now replace the middle term 19x with -2x%2B21x. Remember, -2 and 21 add to 19. So this shows us that -2x%2B21x=19x.


14x%5E2%2Bhighlight%28-2x%2B21x%29-3 Replace the second term 19x with -2x%2B21x.


%2814x%5E2-2x%29%2B%2821x-3%29 Group the terms into two pairs.


2x%287x-1%29%2B%2821x-3%29 Factor out the GCF 2x from the first group.


2x%287x-1%29%2B3%287x-1%29 Factor out 3 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%282x%2B3%29%287x-1%29 Combine like terms. Or factor out the common term 7x-1


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So 2%2814x%5E2%2B19x-3%29 then factors further to 2%282x%2B3%29%287x-1%29


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Answer:


So 28x%5E2%2B38x-6 completely factors to 2%282x%2B3%29%287x-1%29.


In other words, 28x%5E2%2B38x-6=2%282x%2B3%29%287x-1%29.


Note: you can check the answer by expanding 2%282x%2B3%29%287x-1%29 to get 28x%5E2%2B38x-6 or by graphing the original expression and the answer (the two graphs should be identical).

Answer by lenny460(1073) About Me  (Show Source):
You can put this solution on YOUR website!
Factor completely:
28x^2 + 38x - 6
Factor out the Greatest Common Factor (GCF) = 2
2(14x^2 + 19x - 3)
Factor a trinomial:
2(2x + 3)(7x - 1)
The Answer:
2(2x + 3)(7x - 1)