SOLUTION: how to solve Binomial, Trinomial, and 4 term polynomial equations Ex- y^2-5y+4 Ex-3b^2-20b=7 Ex-c^3-125

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Question 159301: how to solve Binomial, Trinomial, and 4 term polynomial equations
Ex- y^2-5y+4
Ex-3b^2-20b=7
Ex-c^3-125
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor these? I'll do the first one to get you started




Looking at the expression y%5E2-5y%2B4, we can see that the first coefficient is 1, the second coefficient is -5, and the last term is 4.


Now multiply the first coefficient 1 by the last term 4 to get %281%29%284%29=4.


Now the question is: what two whole numbers multiply to 4 (the previous product) and add to the second coefficient -5?


To find these two numbers, we need to list all of the factors of 4 (the previous product).


Factors of 4:
1,2,4
-1,-2,-4


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


These factors pair up and multiply to 4.
1*4
2*2
(-1)*(-4)
(-2)*(-2)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -5:


First NumberSecond NumberSum
141+4=5
222+2=4
-1-4-1+(-4)=-5
-2-2-2+(-2)=-4



From the table, we can see that the two numbers -1 and -4 add to -5 (the middle coefficient).


So the two numbers -1 and -4 both multiply to 4 and add to -5


Now replace the middle term -5y with -y-4y. Remember, -1 and -4 add to -5. So this shows us that -y-4y=-5y.


y%5E2%2Bhighlight%28-y-4y%29%2B4 Replace the second term -5y with -y-4y.


%28y%5E2-y%29%2B%28-4y%2B4%29 Group the terms into two pairs.


y%28y-1%29%2B%28-4y%2B4%29 Factor out the GCF y from the first group.


y%28y-1%29-4%28y-1%29 Factor out 4 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.


%28y-4%29%28y-1%29 Combine like terms. Or factor out the common term y-1

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Answer:


So y%5E2-5y%2B4 factors to %28y-4%29%28y-1%29.


Note: you can check the answer by FOILing %28y-4%29%28y-1%29 to get y%5E2-5y%2B4 or by graphing the original expression and the answer (the two graphs should be identical).