SOLUTION: In my college class right now we are learning about polynomials, trinomials, and so on. I am really confused because we are supposed to factor these types of equations and I cannot

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: In my college class right now we are learning about polynomials, trinomials, and so on. I am really confused because we are supposed to factor these types of equations and I cannot      Log On


   

Question 644537: In my college class right now we are learning about polynomials, trinomials, and so on. I am really confused because we are supposed to factor these types of equations and I cannot understand any of the reading materials that have been provided, can someone teach me how to factor trinomials and polynomials?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here's an example:

Factor 5x%5E2+%2B+42x+%2B+16



Looking at the expression 5x%5E2%2B42x%2B16, we can see that the first coefficient is 5, the second coefficient is 42, and the last term is 16.


Now multiply the first coefficient 5 by the last term 16 to get %285%29%2816%29=80.


Now the question is: what two whole numbers multiply to 80 (the previous product) and add to the second coefficient 42?


To find these two numbers, we need to list all of the factors of 80 (the previous product).


Factors of 80:
1,2,4,5,8,10,16,20,40,80
-1,-2,-4,-5,-8,-10,-16,-20,-40,-80


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


These factors pair up and multiply to 80.
1*80 = 80
2*40 = 80
4*20 = 80
5*16 = 80
8*10 = 80
(-1)*(-80) = 80
(-2)*(-40) = 80
(-4)*(-20) = 80
(-5)*(-16) = 80
(-8)*(-10) = 80

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 42:


First NumberSecond NumberSum
1801+80=81
2402+40=42
4204+20=24
5165+16=21
8108+10=18
-1-80-1+(-80)=-81
-2-40-2+(-40)=-42
-4-20-4+(-20)=-24
-5-16-5+(-16)=-21
-8-10-8+(-10)=-18



From the table, we can see that the two numbers 2 and 40 add to 42 (the middle coefficient).


So the two numbers 2 and 40 both multiply to 80 and add to 42


Now replace the middle term 42x with 2x%2B40x. Remember, 2 and 40 add to 42. So this shows us that 2x%2B40x=42x.


5x%5E2%2Bhighlight%282x%2B40x%29%2B16 Replace the second term 42x with 2x%2B40x.


%285x%5E2%2B2x%29%2B%2840x%2B16%29 Group the terms into two pairs.


x%285x%2B2%29%2B%2840x%2B16%29 Factor out the GCF x from the first group.


x%285x%2B2%29%2B8%285x%2B2%29 Factor out 8 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.


%28x%2B8%29%285x%2B2%29 Combine like terms. Or factor out the common term 5x%2B2


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


Answer:


So 5x%5E2%2B42x%2B16 factors to %28x%2B8%29%285x%2B2%29.


In other words, 5x%5E2%2B42x%2B16=%28x%2B8%29%285x%2B2%29.


Note: you can check the answer by expanding %28x%2B8%29%285x%2B2%29 to get 5x%5E2%2B42x%2B16 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, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
--------------------------------------------------------------------------------------------------------------