Question

Can someone help me with this problem involving factoring a trinomial and filling in a table? Steps 1, 2, and 3 please. Thank you!

Answer 1

Step 1 involves you listing out all the ways to multiply to 56, and then adding up those factors. For instance, the first row has 1 and 56 which add to 57 in the third column. The second row has -1 + (-56) = -57. The third row has 2+28 = 30. And so on. The idea is to fill out the table completely with the other ways to have factors of 56 added up. The table is shown in the attached image below.

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Step 2 then uses the table to figure out which pair of factors (of 56) add to -15. This would be -7 and -8. In other words,

-7 plus -8 = -15

-7 times -8 = 56

We have found the right pair of numbers. In the table I have provided, this is shown as the highlighted yellow row.

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Step 3 is then using those pair of numbers found in step 2 to set up the factorization. We would say that x^2-15x+56 factors to (x-7)(x-8). This is the same as (x-8)(x-7) as we can multiply two numbers in any order we want.