Question 148757This question is from textbook
: How do I factor this trinomoial:
5x^2+16x+3
This question is from textbook
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
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 :
1,3,5,15
-1,-3,-5,-15
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to . For instance,  ,  , etc.
Since is positive, this means that either
a) both factors are positive, or...
b) both factors are negative.
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 | 15 | 1+15=16 | | 3 | 5 | 3+5=8 | | -1 | -15 | -1+(-15)=-16 | | -3 | -5 | -3+(-5)=-8 |
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 .
Note: you can check the answer by FOILing to get or by graphing the original expression and the answer.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! factor this trinomial:
5x^2+16x+3
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Using the AC Method of Factoring:
Find two numbers whose product is 3*5 = 15
and whose sum is 16:
The numbers are 15 and 1
Rewrite the problem as follows:
5x^2+15x+x+3
Factor the 1st two and the last two terms seperately:
5x(x+3) + (x+3)
Factor again:
(x+3)(5x+1)
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Cheers,
Stan H.
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