Question 248456: I just learned this today and not sure how to do this. Please help. I have a quiz tomorrow on it. It is factoring. Thank you!!
56-15z+z^2
Found 3 solutions by jim_thompson5910, checkley77, jsmallt9:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!  Start with the given expression.
 Rearrange the terms in descending degree.
Looking at the expression , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,4,7,8,14,28,56
-1,-2,-4,-7,-8,-14,-28,-56
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*56 = 56
2*28 = 56
4*14 = 56
7*8 = 56
(-1)*(-56) = 56
(-2)*(-28) = 56
(-4)*(-14) = 56
(-7)*(-8) = 56
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | 56 | 1+56=57 | | 2 | 28 | 2+28=30 | | 4 | 14 | 4+14=18 | | 7 | 8 | 7+8=15 | | -1 | -56 | -1+(-56)=-57 | | -2 | -28 | -2+(-28)=-30 | | -4 | -14 | -4+(-14)=-18 | | -7 | -8 | -7+(-8)=-15 |
From the table, we can see that the two numbers  and  add to (the middle coefficient).
So the two numbers and both multiply to and add to
Now replace the middle term  with  . Remember, and add to . So this shows us that  .
 Replace the second term with .
 Group the terms into two pairs.
 Factor out the GCF  from the first group.
 Factor out  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.
 Combine like terms. Or factor out the common term 
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Answer:
So factors to .
In other words,  .
Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
Answer by checkley77(12844) (Show Source):
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! First, let's put this expression in order:
This is a quadratic trinomial. Quadratic because of the squared term and trinmoial because the expression has three terms. It has a leading coefficient (i.e. the coefficient of the squared term) which is 1 and that makes this one of the easy quadratic trinomials to factor. Factoring expressions like this one comes down to answering the question: "What are the factors of the constant term (the one at the end without a variable) that add up the the coefficient of the middle term?
In this expression the question is: "What are the factors of 56 that add up to -15?" To answer this question we need to realize that in order for the product to be positive, the two factors must both be positive or both be negative. Since we want them to add up to -15, we will look for two negative factors of 56. With some thought about the factors of 56 it shouldn't take us long to figure out that -7 and -8 are the two factors we are looking for. So:
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