trinomial

[behrens1]

Choose three integers a, b, and c. (Negative numbers are welcome.) Now use a, b, and c to create a trinomial ax2+bx+c. Can you factor this trinomial? How would you create a trinomial that will factor?

I don't understand how to answer this question?

 

[Denis]

Not sure exactly what's being asked either;
guess you can set up the zeroes any way you like:
as example: (2x - 3)(x - 5) = 0
multiply: 2x^2 + 7x - 15 = 0
and you know 2x - 3 = 0 or x - 5 = 0

 

[lookagain]

Choose three integers a, b, and c. (Negative numbers are welcome.) Now use a, b, and c to create a
trinomial ax2+bx+c. Can you factor this trinomial? How would you create a trinomial that will factor?

I don't understand how to answer this question?

behrens1,

And if you choose some arbitrary integers \(\displaystyle a, b, c,\) then the trinomial you form might not factor
(over the integers).

\(\displaystyle The \ discriminant \ of \ the \ quadratic \ \ (ax^2 + bx + c) \ \ is \ \ (b^2 - 4ac).\)

If you choose integer values that make this discriminant equal to a perfect square (and that is to include \(\displaystyle 0\)),
then the resulting trinomial quadratic will factor (over the integers.)

- - Edit - -

 

[Deleted member 4993]

The original problem wants a trinomial. In that case, the condition should be:

\(\displaystyle a \ne 0\)

AND

\(\displaystyle b \ne 0\)

AND

\(\displaystyle c \ne 0\)