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x^2 - 6x + 18.

This looks tempting to factor by guessing.

We want to factor into the form (1x + a) * (1x + b) + c

We guess that both x's have a scalar constant of 1, because x^2 has a scalar constant of 1 in the expanded form. This doesn't have to be the case, but it is a convenient assumption to make.

We want a and b such that (a + b) = -6.

A good choice for this is a = -3, b = -3

a * b = 9, so we need c to cover the distance between 9 and 18. c = 9

So we have:

(x - 3) * (x - 3) + 9

Double checking to make sure we did everything right:

x ^ 2 - 3x - 3x + 9 + 9

x^2 - 6x + 18

You can also complete the square, if you prefer.

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13y ago

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Q: Can you factor x2-6x plus 18?
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