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Find the constant coefficient when the polynomial $\(3(x - 4) + 2(x^2 - x + 7) - 5(x - 1)\)$ is simplified.

 Jul 27, 2018
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Simplify the following:
3 (x - 4) + 2 (x^2 - x + 7) - 5 (x - 1)

3 (x - 4) = 3 x - 12:
3 x - 12 + 2 (x^2 - x + 7) - 5 (x - 1)

2 (x^2 - x + 7) = 2 x^2 - 2 x + 14:
-12 + 3 x + 2 x^2 - 2 x + 14 - 5 (x - 1)

-5 (x - 1) = 5 - 5 x:
2 x^2 + 3 x - 2 x + 5 - 5 x - 12 + 14

Grouping like terms, 2 x^2 + 3 x - 2 x - 5 x - 12 + 5 + 14 = 2 x^2 + (3 x - 2 x - 5 x) + (-12 + 14 + 5):
2 x^2 + (3 x - 2 x - 5 x) + (-12 + 14 + 5)

3 x - 2 x - 5 x = -4 x:
2 x^2 + -4 x + (-12 + 14 + 5)

-12 + 14 + 5 = 7:

 2x^2 - 4x + 7 - The "Constant Coefficient" is 7.

 Jul 27, 2018

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