4. Factor polynomial completely?

Question

16x^2 - 4x -2

Answer 1

16x^2 - 4x - 2
= (4x)^2 -(4x)- 2
= {(4x)^2 - 1} - (4x+1)
={(4x+1)(4x-1)} - (4x+1)
=(4x+1)(4x-2)
= 2*(4x+1)(2x-1)

Answer 2

16x^2 - 4x -2
present -4x as an addition of 2 numbers, one should have sth in common with 16x^2 and the other with 2; for example, -8x and 4x will do the trick:
= 16x^2 - 8x + 4x - 2
now we can pair the obvious (16x^2 and 8x; 4x and 2), and extract the common multipliers
= 8x (2x - 1) + 2 (2x - 1)
put (2x-1) as a common multiplier, and put the rest into brackets:
= (2x - 1)(8x + 2)
the second brackets show that we can extract 2:
= (2x - 1)2(4x + 1)
let's order them neatly:
= 2(2x - 1)(4x + 1)

Check:
16x^2 - 4x -2 = 2(2x - 1)(4x + 1)
= 2(2x*4x + 2x*1 - 1*4x - 1*1)
= 2(8x^2 + 2x - 4x - 1)
= 2(8x^2 - 2x -1)
= 2*8x^2 - 2*2x - 2*1
= 16x^2 - 4x - 2 => left and right sides are equal!
Done!

Answer 3

16x^2 - 4x -2
2[8x^2 - 2x - 1]
2[2x - 1][4x + 1]

See the lesson at the link below

Answer 4

First take out a 2

(2)(8x^2-2x-1)

Then facor out

(2) (4x+1) (2x-1)

Answer 5

2(8x^2-2x-1)
=2(4x+1)(2x-1)