Question

MEDAL!! ALGEBRA HELP!

Given the polynomial 6x3 + 4x2 − 6x − 4, what is the value of the coefficient 'k' in the factored form?

6x3 + 4x2 − 6x − 4 = 2(x + k)(x − k)(3x + 2)

k= ____________

Answer 1

I would recommend dividing out the factors already given, and see what remains.

Answer 2

How do I do that? @Evoker

Answer 3

well basically the process is just like long division

Answer 4

But first taking out the 2 gives, 3x^3+2x^2-3x-2

Answer 5

So I just solve that?

Answer 6

I'm working on an illustration now of the first step

Answer 7

ok here is the initial setup, so now you ask what times 3x gives 3x^3

Answer 8

9?

Answer 9

or to put it another way what is 3x^3/3x

Answer 10

*(3x^3)/(3x)

Answer 11

I'm confused rip

Answer 12

what does 3x^3 equal

Answer 13

\[\frac{ 3x^3 }{3x }\]

Answer 14

oh sorry to answer your question 3 x^3 means 3 times x cubed.

Answer 15

Have to go for a bit

Answer 16

so anyways that yields x^2, so you put that above the first element and then multiply x^2 times 3x+2 and put it under the equation, as shown below

Answer 17

Then you subtract

Answer 18

Since this yields 0, we move to the next non zero term, and repeat the process.

Answer 19

Ohhhh that's what I kept getting and I was confused

Answer 20

so you are left with x^2-1

Answer 21

that factors into x+1 and x-1

Answer 22

So does it equal 1?

Answer 23

That is correct

Answer 24

Thank you so much :)