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The factor theorem is the remainder theorem's zero case: (x − a) divides P(x) exactly when P(a) = 0. Dividing out then reduces the degree by one, ready for further factorising.
Factor theorem
(x − a) is a factor of P(x) ⇔ P(a) = 0
P(1) = 1 − 6 + 11 − 6 = 0, so yes, and the quotient is x² − 5x + 6.
Use the rational root theorem: test factors of the constant term divided by factors of the leading coefficient.