To factor the quadratic polynomial \(x^2 - 7x + 6\), we need to find two numbers that multiply to the constant term \(6\) and add up to the coefficient of the linear term \(-7\).
The numbers that satisfy these conditions are \(-6\) and \(-1\), since:
\[ -6 \times -1 = 6 \quad \text{and} \quad -6 + (-1) = -7 \]
With these two numbers, we can express the polynomial in factored form:
\[ x^2 - 7x + 6 = (x - 6)(x - 1) \]
Thus, the quadratic polynomial \(x^2 - 7x + 6\) can be decomposed into linear factors as:
\[ (x - 6)(x - 1) \]
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