How do you factor 8x^2 - 16x + 6 = 0?

2 Answers

x = 1/2, 3/2

Explanation:

We have,

color(white)(xxx)8x^2 - 16x + 6 = 0

rArr 2(4x^2 - 8x + 3) = 0 [Take 2 as common]

rArr 4x^2 - 8x + 3 = 0 [Divide both sides by 2]

rArr 4x^2 - (2 + 6)x + 3 = 0 [Break 8 as 2 + 6]

rArr 4x^2 - 2x - 6x + 3 = 0 [Use Distributive Property]

rArr 2x(2x - 1) - 3(2x - 1) = 0 [Group the like terms]

rArr (2x - 1)(2x - 3) = 0 [Again Group the like terms]

Now, We know, when the product of two real numbers is zero, then one of them or both of them are zero.

So,

If 2x - 1 = 0 rArr 2x = 1 rArr x = 1/2

And If 2x - 3 = 0 rArr 2x = 3 rArr x = 3/2

So, The solution is x = 1/2, 3/2.

Hope this helps.

Apr 9, 2018

(2x-3)(4x-2)

Try to focus on the factors of 8 and the factors of 6. The -16 will come if you keep trying. Also, keep in mind that it is a negative 16.

Explanation:

I solved this by thinking to myself...

Okay, what are some factors of 8?

2 xx 4

1 xx 8

Usually, the outermost numbers don't seem to work so I tried 2 and 4 on my first try. I knew that the 8 had to be positive so both of these numbers had to be negative or they both had to be positive.

Then, I thought about factors of six, knowing that the six must be positive.

1 xx 6

2 xx 3

(or the negative versions of these)

But since I knew that the middle coefficient was -16, I figured I would try the negative numbers first.

(2x - 3) (4x - 2)

I chose this order of the numbers because I knew that it would be difficult to get a sixteen, since it is considerably larger than these numbers. This is why I chose the 3 to be in the opposite set of numbers than the 4.

Knowing that I could get -12 from this set. With time you will become better at factoring.