Question

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:

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

@joannaayala17 follow @amistre64, please

Answer 5

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

Answer 6

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

Answer 7

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
\[-4=2 \times k \times (-k) \times2\]

Answer 8

sorry \[ax^3+bx^2+cx+d\] is what I mean

Answer 9

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

Answer 10

and then compare