Match the reasons with the statements.

GIVEN: x2 + 6x + 2x + 12 = 0
TO PROVE: x = -6 or x = -2
1. x2 + 6x + 2x + 12 = 0 Combining like terms

2. x2 + 8x + 12 = 0 Distributive Postulate

3. (x + 6)(x + 2) = 0 Zero product postulate

4. x + 6 = 0 or x + 2 = 0 Subtraction property of equality

5. x = -6 or x = -2 Given

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Answer:

Concept: Mathematical Derivation

  1. We are given x^2 +6x+2x+12
  2. Hence we simplify: x^2 + 8x +12
  3. Now we factor: (x+2)(x+6)
  4. By mathematical logic we now proved that the roots are x=-2 and x=-6
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