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Algebra problem solving

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3 Answers

to factor the given expression
this is in the form ax^2 + bx + c
find a*c then use factors of ac that add up to b also pay attention to the signs.
express the middle term with the terms added
regroup and factor out what is common
 
2k^2+7k+3
a = 2; b = 7 and c = 3
ac = 6 what are the factors of 6 that add up to 7? use +6 and +1
2k^2 + 6k + k + 3
group and factor
2k^2 + 6k and k + 3
2k(k+3) + 1(k + 3)  here k + 3 is common to both groups
(2k + 1)(k + 3)
 
I am guessing that the question here is to factor the given expression:
 
2k^2+7k+3
 
Let us set this up as the multiplication of two binomials:
 
We have two possibilities:
A: (2k + 3) (k + 1)
 
or
 
B: (2k + 1) (k + 3)
 
For the first possible solution (A), the k-term will work out to be (2k)(1) + 3(k) = 5k which is not the middle term of the starting expression so this does not look good.
 
For the Second possible solution (B), the k-term will work out to be (2k)(3) + 1(k) = 7k which is the middle term of the starting expression so this is the answer: (2k + 1) (k + 3)
 
 

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