Step 1
Given:
A polynomial is factored completely when it is written as product of prime polynomials.
FOIL METHOD :
To factorize
Substitute 3k-1 = x
The equation becomes,
Using Foil method, AC=7 and BD=-8
The positive factors of 7 are 1 and 7.
Because the middle term has the positive coefficient and the last only the combination of term has a negative coefficient, we consider negative and positive factors of -8.
The possibilities of -8 are 1 and -8 or -1 and 8 or 2 and -4 or 4 and -2.
Step 2
Now we try various arrangements of these factors until we find one that gives the correct coefficient of x.
We first take the possibilities 1 and 7 and 1 and -8 and check the answer,
Answer is incorrect.
We take the possibilities 7 and 1 and 1 and -8 and check :
Answer is incorrect
We take the possibilities 7 and 1 , and -2 and 4 and check :
Answer is correct.
So, the factor of is (7x-2)(x+4)
Step 3
Now, again substitute 3k-1 = x
=(7(3k-1)-2)(3k-1+4)
=(21k-7-2)(3k+3)
=(21k-9)(3k+3)
Take out common term outside,
21k-9=3(7k-3)
3k+3=3(k+1)
(21k-9)(3k+3)=3(7k-3)3(k+1)
=9(7k-3)(k+1)
Therefore, the factor of is 9(7k-3)(k+1)