## anonymous one year ago 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= ____________ Numerical Answers Expected! Answer for Blank 1:

1. anonymous

$6 x^3+4x^2-6x-4=2[3x^3+2x^2-3x-2]=2[(3x^3+2x^2)-1(3x+2)]$ $=2[x^2(3x+2)-1(3x+2)]$ =?

2. anonymous

im sorry i really dont understand how to do any of this..

3. amistre64

the simplest process is to just expand the right side, and compare coefficients

4. Loser66

5. amistre64

as a test, lets try this: let x=0 what do we end up with?

6. amistre64

0+0+0-4 = 2(0+k)(0-k)(0+2)

7. anonymous

It's a polynomial of the form $ax^3+bx^3+c+d$ Consider the "d" term on both the sides Now obviously on the left side this term is -4 on the right side it, it can be obtained be multiplying all constants together, note k is a constant and not a variable $-4=2 \times k \times (-k) \times2$

8. anonymous

sorry $ax^3+bx^2+cx+d$ is what I mean

9. anonymous

If you're having trouble you can always expand all the parenthesis

10. anonymous

and then compare