Question

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

Answer 1

`(4x-1)^2`

Explanation:

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

Answer 2

`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)`