x^2 - 8x + 16 = 0
(x )(x )
You need two numbers that when multiplied are equal to 16, and when added are equal to 8.
These two numbers are 4 and 4 (4 * 4 = 16, 4 + 4 = 16)
Then you need to figure out if these are positive or negative. Since 16 is positive, you know that the numbers are either both positive or both negative. Since the 8 is negative, you know they must be negative.
(x - 4)*(x - 4)
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Find factors of 16 which add to 8: Factors of 16 are 1 & 16, 2 & 7 and 4 & 4: Only the last add to 8 so: (x + 4)(x + 4) or (x + 4)2
That factors to (x^3 + 64)(x^3 + 64) which factors to (x + 4)(x + 4)(x^2 - 4x + 16)(x^2 - 4x + 16)
It is 112
(x + 8)(x + 2)
It equals 113.