Question

Find all the values of k so that the trinomial can be factored using integers.

x^2+kx-19

Answer 1

Use the discriminant
\[\sqrt{b^2-4ac}\]

Answer 2

whats that....

Answer 3

It says integers, so it has to be real.

Answer 4

well it says integers, so they have to be integers

Answer 5

The discriminant has to equal to zero

Answer 6

So \[k^2+4(19)=0\]

Answer 7

there are not too many factors of \(-19\)

Answer 8

The discriminant is without the square root sign sorry.

Answer 9

it is either \((x+19)(x-1)\) or \((x-19)(x+1)\)

Answer 10

so the thing would be 19,-19?

Answer 11

multiply these two out, see what you get for the middle term

Answer 12

lol i dont get it

Answer 13

you have \(x^2+kx-19\) and you want to know what \(k\) is so that this will factor
so it has to look like either \((x+19)(x-1)\) which is one way to factor, or else it must look like \((x-19)(x+1)\) there is no other way because there are not any more integers whose product is \(-19\)

Answer 14

multiply the first one out and you get
\[(x+19)(x-1)=x^2+19x-x-19=x^2+18x-19\] so \(k\) could be \(18\)

Answer 15

your last job is to multiply out
\[(x-19)(x+1)\]and see what you get for the middle term