Question

Hi! Here's my problem, I'm trying to find factors of polynomials given one of their factors. Here's the example: x^4 + 2x^2 - 8x - 16, x + 2

Answer 1

@ertdre
Help please?

Answer 2

to find the other factor of this polynomial, do (x^4+2x^2-8x-16)/x+2

Answer 3

you are trying to find what times x+2 gives you x^4+2x^2-8x-16

Answer 4

Tell me what you get, ask me if you have questions

Answer 5

Okay. I'll be back in a second.

Answer 6

Yup, still confused.
I synthetically divided with -2
and got x^3 -8
Where do I go from here?

Answer 7

did you ever learn how to do polynomial division?

Answer 8

Algebra Two w/ Trig is the course I'm taking right now...

Answer 9

im a freshman taking bc calc, but did you ever learn how to divide a polynomia, by another equation?

Answer 10

example: x^2-4 divided by x+2

Answer 11

Oh, I know how to divide synthetically and how to divide long. What I don't know how to do is how to find factors through dividing, even with given a factor.

Answer 12

so basically, a factor is only one half. A factor needs to be multiplied by another factor to reach the end product. Since we are given the end product, we must divide it by the factor that we are given to find the other factor.

Answer 13

sorry if that made no sense

Answer 14

perhaps an example will help

Answer 15

say we are given the number 30, and that 5 is one of its factors

Answer 16

we need to find another factor

Answer 17

since 5*some number= 30, we can say 5x=30

Answer 18

then divide both sides by 5, which gives us x=6 as another factor

Answer 19

it is the same with this problem

Answer 20

x+2 * some number = x^4+2x^2-8x-16

Answer 21

so we divide both sides by x+2 to find the "some number"

Answer 22

some number= (x^4+2x^2-8x-16)/(x+2)

Answer 23

then since you know polynomial division, do x^4+2x^2-8x-16 divided by x+2 to find your answer

Answer 24

But I already did. That's how I got x^3 - 8, and I want to know how to find more factors.

Answer 25

how did you get x^3-8? That doesn't seem right