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The factors of \( x^{2} - 5x + 6 \) are \( (x - 2) \) and \( (x - 3) \).
Solución
To factor the quadratic expression x² - 5x + 6, we look for two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of x).
Step 1: List the pairs of numbers that multiply to 6:
• 1 and 6
• 2 and 3
Step 2: Find which pair adds up to -5.
Since the sum is negative and the product is positive, both numbers must be negative. Consider -2 and -3:
• (-2) × (-3) = 6
• (-2) + (-3) = -5
Step 3: Rewrite the quadratic expression using these numbers:
x² - 5x + 6 = (x - 2)(x - 3)
Thus, the factors of x² - 5x + 6 are (x - 2) and (x - 3).
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Simplifique esta solución Mind Expander
To factor the quadratic expression \( x^{2} - 5x + 6 \), you're looking for two numbers that multiply to \( 6 \) (the constant term) and add up to \( -5 \) (the coefficient of \( x \)). The numbers \( -2 \) and \( -3 \) fit the bill! So, you can write the factored form as \( (x - 2)(x - 3) \). This means if you set the factors to zero, you'll find the roots of the equation: \( x = 2 \) and \( x = 3 \). Now, if you wanted to verify your factored form, just expand \( (x - 2)(x - 3) \) back out: \( x^2 - 3x - 2x + 6 = x^2 - 5x + 6 \). Voilà! You've got your original expression back. It's like a little math magic show!
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