SOLUTION: I have a problem I need worked out and I do not understand it. I need it step by step please. It is factor each trinomial using the ac method. I hope someone can help me. 21x^2+

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I have a problem I need worked out and I do not understand it. I need it step by step please. It is factor each trinomial using the ac method. I hope someone can help me. 21x^2+      Log On


   

Question 380373: I have a problem I need worked out and I do not understand it. I need it step by step please. It is factor each trinomial using the ac method. I hope someone can help me.
21x^2+2x-3
Thank you so much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 21x%5E2%2B2x-3, we can see that the first coefficient is 21, the second coefficient is 2, and the last term is -3.


Now multiply the first coefficient 21 by the last term -3 to get %2821%29%28-3%29=-63.


Now the question is: what two whole numbers multiply to -63 (the previous product) and add to the second coefficient 2?


To find these two numbers, we need to list all of the factors of -63 (the previous product).


Factors of -63:
1,3,7,9,21,63
-1,-3,-7,-9,-21,-63


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


These factors pair up and multiply to -63.
1*(-63) = -63
3*(-21) = -63
7*(-9) = -63
(-1)*(63) = -63
(-3)*(21) = -63
(-7)*(9) = -63

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 2:


First NumberSecond NumberSum
1-631+(-63)=-62
3-213+(-21)=-18
7-97+(-9)=-2
-163-1+63=62
-321-3+21=18
-79-7+9=2



From the table, we can see that the two numbers -7 and 9 add to 2 (the middle coefficient).


So the two numbers -7 and 9 both multiply to -63 and add to 2


Now replace the middle term 2x with -7x%2B9x. Remember, -7 and 9 add to 2. So this shows us that -7x%2B9x=2x.


21x%5E2%2Bhighlight%28-7x%2B9x%29-3 Replace the second term 2x with -7x%2B9x.


%2821x%5E2-7x%29%2B%289x-3%29 Group the terms into two pairs.


7x%283x-1%29%2B%289x-3%29 Factor out the GCF 7x from the first group.


7x%283x-1%29%2B3%283x-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.


%287x%2B3%29%283x-1%29 Combine like terms. Or factor out the common term 3x-1


===============================================================


Answer:


So 21x%5E2%2B2x-3 factors to %287x%2B3%29%283x-1%29.


In other words, 21x%5E2%2B2x-3=%287x%2B3%29%283x-1%29.


Note: you can check the answer by expanding %287x%2B3%29%283x-1%29 to get 21x%5E2%2B2x-3 or by graphing the original expression and the answer (the two graphs should be identical).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim