Given the polynomial 6x3 + 4x2 − 6x − 4, what is the value of the constant 'k' in the factored form? 6x3 + 4x2 − 6x − 4 = 2(x + k)(x − k)(3x + 2) k= numerical answers expected! answer for blank 1:

First you graph it using a graphing calculator, you look at the table of values to find out one point in which y= 0. The first one that comes up is when x=1.
If you don't have a graphing calculator you can use trial and error by inputing some numbers into x until you get y= 0. 

Once you have an x value which makes y=0, you can start factorizing it. 
you divide 6x3 +4x2 -6x - 4 into (x-1) which is when y =0 
to get 6x2+10x+4 

This can be used to write the polynomial as (x-1)(6x2 +10x+4) 
you then factorize the second bracket, 6x2 +10x+4.
you can take the 2 outside to give you 2(3x2 +5x+2) 
you can factorize this to become 2(3x+2)(x+1) 

Now you just substitute your factorized second bracket into your unfactorized second bracket to give you 2(3x+2)(x+1)(x-1).

From this you can deduce that k= 1