Question

What is the solution interval of x³ – 2x^2 – 9x + 18 > 0?

Answer 1

need to factor x^3-2x^2-9x+18 first.

Answer 2

You can do this by attempting to factor by grouping.

Answer 3

How would i factor it ?

Answer 4

by grouping

Answer 5

group the first two terms together and factor what they have in common out of the first two terms
group the second two terms and do the same

Answer 6

factor x^3-2x^2
factor -9x+18

Answer 7

x^2(x-2)
(x-9) (x+2)

Answer 8

would it be like that ?

Answer 9

have you factor x^3-2x^2 yet?

Answer 10

oh was it x^2(x-2)? ok that looks good

but you still need to factor -9x+18

Answer 11

im trying. dont you take out the x^2 or just the x ?

Answer 12

or do you just factor out the x ?
i came up with x(x^2-2x+9) what do i do now

Answer 13

-9x and 18
only have the factor 9 in common
so you could factor 9 or -9 out
I'm choosing to factor out -9
so -9x+18=-9(x-2)

Answer 14

\[x^3-2x^2-9x+18 >0 \\ x^2(x-2)-9(x-2)>0\] now we need one more step to finish the factoring up

Answer 15

do you see what factor to factor out?

Answer 16

we have two terms
x^2(x-2)
and
-9(x-2)

Answer 17

would we factor out -2 ?

Answer 18

the factors of x^2(x-2) are x^2 and (x-2)
the factors of -9(x-2) are -9 and (x-2)
both terms only have one factor in common
and no it isn't -2

Answer 19

okay im thinking

Answer 20

i;m asking you to factor and I told you the factors of both terms
to factor something you only need to see what they first have in common as factors