SOLUTION: I am in tears over how to solve these. Please help! I need someone to explain this to me in very simple step-by-step terms. My math book is completely confusing as are some of the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am in tears over how to solve these. Please help! I need someone to explain this to me in very simple step-by-step terms. My math book is completely confusing as are some of the       Log On


   

Question 590755: I am in tears over how to solve these. Please help! I need someone to explain this to me in very simple step-by-step terms. My math book is completely confusing as are some of the math tutorials I have watched.
Factor:
20s^2 + 11s - 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 20s%5E2%2B11s-3, we can see that the first coefficient is 20, the second coefficient is 11, and the last term is -3.


Now multiply the first coefficient 20 by the last term -3 to get %2820%29%28-3%29=-60.


Now the question is: what two whole numbers multiply to -60 (the previous product) and add to the second coefficient 11?


To find these two numbers, we need to list all of the factors of -60 (the previous product).


Factors of -60:
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60


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


These factors pair up and multiply to -60.
1*(-60) = -60
2*(-30) = -60
3*(-20) = -60
4*(-15) = -60
5*(-12) = -60
6*(-10) = -60
(-1)*(60) = -60
(-2)*(30) = -60
(-3)*(20) = -60
(-4)*(15) = -60
(-5)*(12) = -60
(-6)*(10) = -60

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 11:


First NumberSecond NumberSum
1-601+(-60)=-59
2-302+(-30)=-28
3-203+(-20)=-17
4-154+(-15)=-11
5-125+(-12)=-7
6-106+(-10)=-4
-160-1+60=59
-230-2+30=28
-320-3+20=17
-415-4+15=11
-512-5+12=7
-610-6+10=4



From the table, we can see that the two numbers -4 and 15 add to 11 (the middle coefficient).


So the two numbers -4 and 15 both multiply to -60 and add to 11


Now replace the middle term 11s with -4s%2B15s. Remember, -4 and 15 add to 11. So this shows us that -4s%2B15s=11s.


20s%5E2%2Bhighlight%28-4s%2B15s%29-3 Replace the second term 11s with -4s%2B15s.


%2820s%5E2-4s%29%2B%2815s-3%29 Group the terms into two pairs.


4s%285s-1%29%2B%2815s-3%29 Factor out the GCF 4s from the first group.


4s%285s-1%29%2B3%285s-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.


%284s%2B3%29%285s-1%29 Combine like terms. Or factor out the common term 5s-1


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Answer:


So 20s%5E2%2B11s-3 factors to %284s%2B3%29%285s-1%29.


In other words, 20s%5E2%2B11s-3=%284s%2B3%29%285s-1%29.


Note: you can check the answer by expanding %284s%2B3%29%285s-1%29 to get 20s%5E2%2B11s-3 or by graphing the original expression and the answer (the two graphs should be identical).

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