Question 336804


{{{8x^2+16x+12}}} Start with the given expression



{{{4(2x^2+4x+3)}}} Factor out the GCF {{{4}}}



Now let's focus on the inner expression {{{2x^2+4x+3}}}





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Looking at {{{2x^2+4x+3}}} we can see that the first term is {{{2x^2}}} and the last term is {{{3}}} where the coefficients are 2 and 3 respectively.


Now multiply the first coefficient 2 and the last coefficient 3 to get 6. Now what two numbers multiply to 6 and add to the  middle coefficient 4? Let's list all of the factors of 6:




Factors of 6:

1,2,3,6


-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to 6

1*6

2*3

(-1)*(-6)

(-2)*(-3)


note: remember two negative numbers multiplied together make a positive 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


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">6</td><td>1+6=7</td></tr><tr><td align="center">2</td><td align="center">3</td><td>2+3=5</td></tr><tr><td align="center">-1</td><td align="center">-6</td><td>-1+(-6)=-7</td></tr><tr><td align="center">-2</td><td align="center">-3</td><td>-2+(-3)=-5</td></tr></table>

None of these pairs of factors add to 4. So the expression {{{2x^2+4x+3}}} cannot be factored


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Answer:

So {{{8x^2+16x+12}}} factors to {{{4(2x^2+4x+3)}}}

    

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