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The quadratic equation x^2 - 3x + 2 = 0 can be factored as?

Practice Questions

Q1
The quadratic equation x^2 - 3x + 2 = 0 can be factored as?
  1. (x-1)(x-2)
  2. (x-2)(x-1)
  3. (x+1)(x+2)
  4. (x-3)(x+2)

Questions & Step-by-Step Solutions

The quadratic equation x^2 - 3x + 2 = 0 can be factored as?
  • Step 1: Start with the quadratic equation x^2 - 3x + 2 = 0.
  • Step 2: Look for two numbers that multiply to the constant term (2) and add up to the coefficient of x (-3).
  • Step 3: The numbers that work are -1 and -2 because (-1) * (-2) = 2 and (-1) + (-2) = -3.
  • Step 4: Rewrite the quadratic equation using these numbers: x^2 - 1x - 2x + 2 = 0.
  • Step 5: Group the terms: (x^2 - 1x) + (-2x + 2) = 0.
  • Step 6: Factor out the common terms: x(x - 1) - 2(x - 1) = 0.
  • Step 7: Now, factor out (x - 1): (x - 1)(x - 2) = 0.
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