# How do you factor #4x^2 - 5x + 1 = 0 #?

##### 1 Answer

Feb 20, 2017

#### Answer:

#### Explanation:

Given:

#4x^2-5x+1 = 0#

**Method 1**

Note that the sum of the coefficients is

#4-5+1 = 0#

Hence

#0 = 4x^2-5x+1 = (x-1)(4x-1)#

**Method 2**

Note that the prime factorisation of

#451 = 11*41#

and this multiplication involves no carrying of digits.

Hence we find:

#4x^2+5x+1 = (x+1)(4x+1)#

and:

#4x^2-5x+1 = (x-1)(4x-1)#

**Method 3**

Note that:

#(ax-1)(bx-1) = abx^2-(a+b)x+1#

Since the constant term of the given example is

Hence we find:

#(4x-1)(x-1) = 4x^2-5x+1#