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

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

Options:

Correct Answer: (x-1)(x-2)

Solution:

The equation factors to (x-1)(x-2) = 0.

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

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.

Factoring Quadratic Equations – The process of rewriting a quadratic equation in the form of a product of two binomials.
Roots of Quadratic Equations – Finding the values of x that satisfy the equation by setting each factor to zero.