Question 119774This question is from textbook Algebra 2 with Trigonometry
: I don't understand how to do trinomials. The problem is w^2+4w-84. The ^ means exponent.Could you please help me answer this question.
This question is from textbook Algebra 2 with Trigonometry
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Do you want to factor?
Looking at  we can see that the first term is  and the last term is  where the coefficients are 1 and -84 respectively.
Now multiply the first coefficient 1 and the last coefficient -84 to get -84. Now what two numbers multiply to -84 and add to the middle coefficient 4? Let's list all of the factors of -84:
Factors of -84:
1,2,3,4,6,7,12,14,21,28,42,84
-1,-2,-3,-4,-6,-7,-12,-14,-21,-28,-42,-84 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -84
(1)*(-84)
(2)*(-42)
(3)*(-28)
(4)*(-21)
(6)*(-14)
(7)*(-12)
(-1)*(84)
(-2)*(42)
(-3)*(28)
(-4)*(21)
(-6)*(14)
(-7)*(12)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4
| First Number | Second Number | Sum | | 1 | -84 | 1+(-84)=-83 | | 2 | -42 | 2+(-42)=-40 | | 3 | -28 | 3+(-28)=-25 | | 4 | -21 | 4+(-21)=-17 | | 6 | -14 | 6+(-14)=-8 | | 7 | -12 | 7+(-12)=-5 | | -1 | 84 | -1+84=83 | | -2 | 42 | -2+42=40 | | -3 | 28 | -3+28=25 | | -4 | 21 | -4+21=17 | | -6 | 14 | -6+14=8 | | -7 | 12 | -7+12=5 |
None of these pairs of factors add to 4. So the expression cannot be factored
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