Factor ^2 - 4x + 4. x^2 - 4x +4=
1 answer:
<h3>Answer: (x-2)(x-2)</h3>
This is the same as
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Explanation:
The middle coefficient is -4 and the last term is 4.
We need to find factors of the last term that add to the middle coefficient.
Here is a list of all ways to multiply two integers to get 4, and the sum of each pair of factors.
- -1 + (-4) = -5
- -2 + (-2) = -4
- 2 + 2 = 4
- 1 + 4 = 5
The second row of that list above is what we're after. So
-2 + (-2) = -4
-2 * (-2) = 4
Meaning the factorization is (x-2)(x-2). Note the "-2" values in each factor
We can use the FOIL rule or distribution to go from (x-2)(x-2) back to x^2-4x+4 to confirm the answer.
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F(x) = (x + 1)(x - 2)
f(x) = x(x - 2) + 1(x - 2)
f(x) = x(x) - x(2) + 1(x) - 1(2)
f(x) = x² - 2x + x - 2
f(x) = x² - x - 2
f(x) = x(x - 2) + 1(x - 2)
f(x) = x(x) - x(2) + 1(x) - 1(2)
f(x) = x² - 2x + x - 2
f(x) = x² - x - 2