How do you factor completely 16x^2-8x+1?

2 Answers
Mia
Jun 16, 2016

(4x-1)^2

Explanation:

This is a polynomial of second degree and since the coefficient of
" "
x<0 , we think of the binomial property that says:
" "
a^2-2ab+b^2=(a-b)^2
" "
In the given polynomial first term 16x^2=(4x)^2and 1=(1)^2
" "
16x^2-8x+1
" "
=(4x)^2-2(4x)(1)+1^2
" "
=(4x-1)^2

EZ as pi
Sep 29, 2017

16x^2 -8x+1

=(4x-1)(4x-1)

Explanation:

The color(lime)(+) sign in the third term indicates two things:

  • the factors need to be color(lime)(ADDED)
  • the signs in the brackets will color(lime)("be the same")

The color(red)(-)sign in the second term indicates that the signs will be negative.

16x^2color(red)(-)8x color(lime)(+) 1

Find factors of 16 and 1 which add to 8.

The factors of 1 are just 1, so we can ignore them.

The factors of 16 which add to 8 are 4 and 4

4xx4 = 16 and 4+4=8

16x^2 -8x+1

=(4x-1)(4x-1)

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