Question 397336


Looking at {{{8t^2-3t-4}}} we can see that the first term is {{{8t^2}}} and the last term is {{{-4}}} where the coefficients are 8 and -4 respectively.


Now multiply the first coefficient 8 and the last coefficient -4 to get -32. Now what two numbers multiply to -32 and add to the  middle coefficient -3? Let's list all of the factors of -32:




Factors of -32:

1,2,4,8,16,32


-1,-2,-4,-8,-16,-32 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -32

(1)*(-32)

(2)*(-16)

(4)*(-8)

(-1)*(32)

(-2)*(16)

(-4)*(8)


note: remember, the product of a negative and a positive number is a negative number



Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">-32</td><td>1+(-32)=-31</td></tr><tr><td align="center">2</td><td align="center">-16</td><td>2+(-16)=-14</td></tr><tr><td align="center">4</td><td align="center">-8</td><td>4+(-8)=-4</td></tr><tr><td align="center">-1</td><td align="center">32</td><td>-1+32=31</td></tr><tr><td align="center">-2</td><td align="center">16</td><td>-2+16=14</td></tr><tr><td align="center">-4</td><td align="center">8</td><td>-4+8=4</td></tr></table>


None of these pairs of factors add to -3. So the expression {{{8t^2-3t-4}}} cannot be factored



So you are correct. Good job.