SOLUTION: how can I factor 4x^2+16x+13?

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Question 270291: how can I factor 4x^2+16x+13?
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 4 and the last term 13 to get 52. Now we need to ask ourselves: What two numbers multiply to 52 and add to 16? Lets find out by listing all of the possible factors of 52

Factors:

1,2,4,13,26,52,

-1,-2,-4,-13,-26,-52, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 52.

1*52=52

2*26=52

4*13=52

(-1)*(-52)=52

(-2)*(-26)=52

(-4)*(-13)=52

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 16

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 First Number | Second Number | Sum 1 | 52 | 1+52=53 2 | 26 | 2+26=28 4 | 13 | 4+13=17 -1 | -52 | -1+(-52)=-53 -2 | -26 | -2+(-26)=-28 -4 | -13 | -4+(-13)=-17

None of these factors add to 16. So the quadratic cannot be factored.