Determine the factors of x2 − 7x − 10.

a. (x + 2)(x − 5)

b. prime

c. (x − 2)(x + 5)

d. (x + 10)(x − 1)

Hey there!

We could try to factor this trinomial by splitting up the middle term. We do this by multiplying the coefficient of the first term, 1x², by the constant, –10. This will get us –10. Next, you would have to find two factors of –10 that add up to the coefficient of the middle term, which is –7. 

Factors of –10:

–10 + 1 = –9
–5 + 2 = –3
–2 + 5 = 3
–1 + 10 = 9

As you can see, no factors of –10 add up to –7. Therefore, this trinomial is prime. In other words, you could only get this trinomial by multiplying it by 1 to get itself. 

Hope this helped you out! :-)

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