Question

for each of the following expressions, determine all of the values of k that allow the trinomial to be factored over integers. 25x@+kx+49

Answer 1

25x^2+kx+49

Answer 2

Is that supposed to be \(25x^2 + kx + 49\) ?

Answer 3

Ok, I see.

Answer 4

25 can be factored as
25 and 1
5 and 5

49 can be factored as
49 and 1
-49 and -1
7 and 7
-7 and -7

Now you need to try every combination of the factors that will give you the first term of 25x^2 and the last term of 49.

(25x + 49)(x + 1)
(25x - 49)(x - 1)
(25x + 7)(x + 7)
(25x - 7)(x - 7)
(5x + 49)(5x + 1)
(5x - 49)(5x - 1)
(5x + 7)(5x + 7)
(5x - 7)(5x - 7)

Now use FOIL on every product above and find the middle term.
All you really need to do is the OI part of FOIL for each product above.
Then combine the terms you get from OI.
These will be all the values you can have for k.

Answer 5

so the first one (25x + 49)(x + 1) i got 74x for the
OI after i combined it. Thats then the value of k?

Answer 6

74?