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17 votes
17 votes
Factor completely.
x² − 8x+16

(-4)²
(z+4)²
2(z + 2)?
2(x - 2)²

User Glauco Cucchiar
by
2.8k points

1 Answer

7 votes
7 votes

Answer:

(x-4)^2 [I assume the (z+4)² option was mistyped. Who wants zzzzzzzzz?]

Explanation:

x² − 8x+16

Lok for a pattern that would allow us to fill in the missing numbers in

(x+a)*(x+b)

We know that a and b must equal +16 when multiplied together. We also know their sum must be -8.

a*b = 16

a+b = -8

Is there anything that ties these numbers together? The number 4 comes to mind: 8 and 16 are known to be friendly to 4. We need the sum to be -8, so lets make the 4 negative and put it into both expressions.

(-4)+(-4) = -8 YES

(-4)*(-4) = 16 YES

Assinging -4 to both a and b produces the factored expression:

(x-4)*(x-4) = x² − 8x+16 YES

User MacNimble
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2.4k points