Factor x^2 - 5x + 6.

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Multiple Choice

Factor x^2 - 5x + 6.

Explanation:
Factoring quadratics by finding two numbers that multiply to the constant term and add to the middle coefficient. For x^2 - 5x + 6, the middle term is -5 and the constant is 6, so we look for two numbers that multiply to 6 and sum to -5. Those numbers are -2 and -3. Rewriting x^2 - 5x + 6 as x^2 - 2x - 3x + 6 lets us factor by grouping: x(x - 2) - 3(x - 2) = (x - 3)(x - 2). Expanding confirms: (x - 3)(x - 2) = x^2 - 5x + 6. Other ways to multiply to 6 give different middle terms (for example, (x - 1)(x - 6) yields -7x, and (x - 4)(x - 2) yields -6x), so they don’t match the original expression.

Factoring quadratics by finding two numbers that multiply to the constant term and add to the middle coefficient. For x^2 - 5x + 6, the middle term is -5 and the constant is 6, so we look for two numbers that multiply to 6 and sum to -5. Those numbers are -2 and -3. Rewriting x^2 - 5x + 6 as x^2 - 2x - 3x + 6 lets us factor by grouping: x(x - 2) - 3(x - 2) = (x - 3)(x - 2). Expanding confirms: (x - 3)(x - 2) = x^2 - 5x + 6. Other ways to multiply to 6 give different middle terms (for example, (x - 1)(x - 6) yields -7x, and (x - 4)(x - 2) yields -6x), so they don’t match the original expression.

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