Question

find three values of k>0 such that x^2-6x+k can be factored

Answer 1

@zepdrix

Answer 2

Ummmm so for it to factor nicely, we need 2 numbers which:
`Multiply to k`
`Add to -6`

Answer 3

So ummmm

Answer 4

Oh I guess it's just as simple as choosing two numbers which add to -6.
Then we multiply those numbers to give us k.

Answer 5

So we could use ummm... how bout,

-4+ -2 = -6 right?

Answer 6

so we need -1 and 6 correct

Answer 7

or 1*-6

Answer 8

If we add those values,
\[\Large -6+1\ne-6\]Hmm I think you're thinking backwards ^^ heh

Answer 9

oh i see it needs to equal -6 so yes we can use -4+-2

Answer 10

If our 2 numbers are -4 and -2, what would our k value be?
It should be the product of those two numbers, yes?

Answer 11

we would get -4+-2=-6

Answer 12

-4 + -2 = -6 gives us that middle number that we needed.

Now to find k, we use the same numbers but we multiply them:
-4 * -2 = ?

Answer 13

8

Answer 14

Ok good! So there is a value of k>0 that will work for our equation.\[\Large x^2-6x+\color{orangered}{8}\quad=\quad (x-4)(x-2)\]

Answer 15

So our first answer is k=8.
We need to come up with a couple more.

Answer 16

alright

Answer 17

One thing to keep in mind, since they're restricting the k value to be positive ( k > 0 ), our numbers will both have to be negative.
(Since neg*neg = pos )

Can you think of two other negative numbers that add to -6 besides -4 and -2?

Answer 18

we could do -2 and-3

Answer 19

-2 + -3 = -5

Hmm that doesn't quite work.

Answer 20

1 and 6

Answer 21

waitt hat dosen't work either

Answer 22

You're still thinking multiplication silly :3

Answer 23

3 an3

Answer 24

-3-3

Answer 25

good good :)

k = -3 * -3

Answer 26

and that would be 9

Answer 27

Ok good we've found 2 values!
k=8
k=9

Answer 28

-1-5=-6

Answer 29

Good good good.

Answer 30

-1*-5=5

Answer 31

sorry for thinking multiplication to much lol

Answer 32

k=5
k=8
k=9

Yayyyy good job \c:/ you found them all!

Answer 33

thanks for the help