Question

find six values of k such that x^2+kx+18 can be factored

Answer 1

the + sign on the last number means the factors will have the same sign (either both negative or both positive)

the first step is list all pairs of numbers that multiply to give you 18
1,18
2,9
3,6

the sum of each pair gives a k
if you make both numbers in each pair negative, you will get 3 more numbers for k

Answer 2

i have that so far

Answer 3

am i also supposed to multiply them

Answer 4

and add

Answer 5

to get 18

Answer 6

we know all those multiplied equal 18

Answer 7

if you multiply them, you get the last number (which is how I got them in the first place)
the sum gives you the middle number.

Answer 8

for example k= 1+18= 19
x^2 + 19 x + 18
factors into (x+1)(x+18)

Answer 9

ok

Answer 10

what other numbers can k be?

Answer 11

it can be 11,9

Answer 12

so that's three found so far

Answer 13

the other "rule" is the + sign on 18 means the factors have the same sign
you listed the plus factors.

you could also have both factors be negative.

Answer 14

and then-9, and -11

Answer 15

and -19

Answer 16

yes and -19

Answer 17

thanks for the help

Answer 18

you should go over this problem, and maybe even multiply out the factors to see how it works.

for example
using k= -9
x^2 -9 x + 18
we used 3 and 6 (they multiply to get 18). the have a minus sign because + on the 18 means the same sign, and the - on the 9x means the largest factor is minus. if the largest factor is minus, and both are the same sign, both factors are minus
-3 and -6
and we write
(x-3)(x-6)
multiply that out to get x^2 -3x-6x+18 = x^2 -9x +18