Factor 16t^2-8t+1

Question

factor the polynomial

Answer 1

You can also factor by grouping (AC method).

 

Find two numbers that multiply to 16 and add to -8.  The numbers are -4 and -4.

 

16t² - 4t - 4t + 1 =

 

4t(4t - 1) - (4t - 1)

 

 

(4t - 1) is a common factor.  The polynomial factors out to be

 

(4t - 1)(4t - 1)

Answer 2

16t² -8t+1

 

= (4t)² -2(4t)(1)+(1)²

 

=(4t-1)² .........    using a² -2ab +b² =(a-b)² 

Answer 3

Notice that if you take the square root of 16t2 you get 4t and -4t.  If you multiply by 2, you get 8t and -8t.