Question

How do you solve 4x^2 -5x +1 = 0 by factoring?

Answer 1

To factor this you have to figure out what times what equal 1, and what plus what equals -5
Because you have middle number as a negative you now know that the two factoring numbers need to be negative.
You also know that the only way you can get one by multiplying is by using two ones together.
This leads you to be almost complete with your factoring.
The last thing you need to to do is figure out how the 4x^2 was created by look at 4's factors.
They are 2*2 and 4*1
With these two factors the only way you would be able to get a 5x is by 4*1

Your final factors are (4x - 1)(x - 1)

Answer 2

$4x^{2}-5x+1=0 \\ \\ 4x^{2}-4x-x+1=0 \\ \\ 4x(x-1)-(x-1)=0 \\ \\ (4x-1)(x-1)=0 \\ \\ 4x-1=0 \ \vee \ x-1=0 \\ \\ 4x=1 \ \vee \ x=1 \\ \\ x= \frac{1}{4} \ \vee \ x=1 \\ \\ x\in \lbrace \frac{1}{4} , 1 \rbrace$

\\\ Ben