To factor the expression x² – 8x + 16 completely, we first look for two numbers that multiply to the constant term (16) and add up to the coefficient of the middle term (-8).
The numbers that satisfy these conditions are -4 and -4, since:
- -4 × -4 = 16
- -4 + -4 = -8
This means we can rewrite the expression as:
(x – 4)(x – 4) or (x – 4)².
So, the completely factored form of the expression is:
(x – 4)²
In conclusion, the expression x² – 8x + 16 factors to (x – 4)², indicating that it has a repeated root at x = 4.