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\( k^{2} - 17k + 16 = (k - 1)(k - 16) \)
Solución
To factor the quadratic expression k² - 17k + 16, we look for two numbers that multiply to 16 (the constant term) and add up to -17 (the coefficient of k).
Notice that -1 and -16 satisfy these conditions because:
(-1) × (-16) = 16
(-1) + (-16) = -17
Thus, we can write:
k² - 17k + 16 = (k - 1)(k - 16)
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Simplifique esta solución Bonus Knowledge
To factor the quadratic \( k^{2}-17k+16 \), we need to find two numbers that multiply to \( 16 \) (the constant term) and add up to \( -17 \) (the coefficient of the linear term). After a little thought, we find that the numbers \( -16 \) and \( -1 \) meet these requirements because \( -16 \times -1 = 16 \) and \( -16 + (-1) = -17 \). Thus, we can write: \[ k^{2}-17k+16 = (k - 16)(k - 1) \] So, the factored form is \( (k - 16)(k - 1) \).
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