Question

Determine the x values that cause the polynomial function to be positive:
f(x)=(x+2)(x+1)(x-5) Determine the x values that cause the polynomial function to be positive:
f(x)=(x+2)(x+1)(x-5) @Mathematics

Answer 1

Set each one greater than zero.. like this\[x + 2 \gt 0\]\[x + 1 \gt 0\]\[x - 5 \gt 0\] solve for x on all three..

x > -2
x > -1
x > 5

so in order for the polynomial to be positive the answer is x > 5

Answer 2

i got that part but the answer also shows -2<x<-1 as an answer and idk how

Answer 3

Ok.. say you choose -1.5..

\[(-1.5 + 2)(-1.5 + 1)(-1.5 - 5)\]\[(.5)(-.5)(-6.5)\]Notice the last two numbers are negative.. a negative times a negative is a positive and the first number is positive therefore \[\large -2 \lt x \lt -1\] is true.

Answer 4

ok that makes sense thanks!

Answer 5

I would of never thought about checking that. lol

Answer 6

haha i was absent when we learned this :P
i dont get this one: f(x)=(x+7)(x+4)(x-6)^2 either lol think you could help?

Answer 7

ok.. Same process as before so ill skip some steps
x > -7
x > -4
(x-6)^2 means (x-6)(x-6) so
x > 6

Answer 8

so for it to be positive x > 6

Answer 9

how we check \[-7 \lt x \lt -4\] and \[-4 \lt x \lt 6\] to see if you get a positive result.

Answer 10

Now***

Answer 11

WHAT. how do you know that is how to check?

Answer 12

we are checking numbers in between to see if we get a positive result..

the first 2 x's are x > -7 and x > -4.. so we check numbers between these numbers

and the last two numbers are x > -4 and x > 6.. so we check between these numbers.

Answer 13

Just like the last problem did.

Answer 14

ok so why dont we check x<-7

Answer 15

because x is positive if x > -7 for the first term.. if it is < -7 then it would be negative.

Answer 16

So the lowest number we need to go is -7.. we dont need to check for any numbers lower than that.

Answer 17

ok. so the answer key says x<-7 or -4<x<6 or x>6... is this right?

Answer 18

i dont see how they got x < -7

Answer 19

hmm ok so what would you say the answer is?

Answer 20

x > 6 for sure

Answer 21

-4 < x < 6 ill have to pick a number and see what i get.

Answer 22

we can pick 1

Answer 23

\[(8)(5)(-5)^2\]

Answer 24

This will be positive because if you square a negative number then it becomes positive.

Answer 25

so -4<x<6 is right too.

Answer 26

ok i think i get it

Answer 27

lets try a number < -7 and see what happens.. ill choose -8\[(-1)(-4)(-14)^2 = positive\] thats weird. Im not sure how they got that one.

Answer 28

hah ya im starting to get what to do now :)

Answer 29

Alright cool lol. Good luck!!

Answer 30

thanks!!