SOLUTION: 2w^2 + 11w - 30 what is the factored form

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: 2w^2 + 11w - 30 what is the factored form      Log On


   

Question 263190: 2w^2 + 11w - 30
what is the factored form
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 2w%5E2%2B11w-30, we can see that the first coefficient is 2, the second coefficient is 11, and the last term is -30.


Now multiply the first coefficient 2 by the last term -30 to get %282%29%28-30%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 11w with -4w%2B15w. Remember, -4 and 15 add to 11. So this shows us that -4w%2B15w=11w.


2w%5E2%2Bhighlight%28-4w%2B15w%29-30 Replace the second term 11w with -4w%2B15w.


%282w%5E2-4w%29%2B%2815w-30%29 Group the terms into two pairs.


2w%28w-2%29%2B%2815w-30%29 Factor out the GCF 2w from the first group.


2w%28w-2%29%2B15%28w-2%29 Factor out 15 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.


%282w%2B15%29%28w-2%29 Combine like terms. Or factor out the common term w-2


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


Answer:


So 2w%5E2%2B11w-30 factors to %282w%2B15%29%28w-2%29.


In other words, 2w%5E2%2B11w-30=%282w%2B15%29%28w-2%29.


Note: you can check the answer by expanding %282w%2B15%29%28w-2%29 to get 2w%5E2%2B11w-30 or by graphing the original expression and the answer (the two graphs should be identical).