Subject: Mathematics
Book: Maths Mastery
The Remainder Theorem states that the remainder when a polynomial f(x) is divided by (x – a) is simply f(a). For example, if you want the remainder when x² – 5x + 6 is divided by (x – 3), evaluate f(3) = 3² – 5×3 + 6 = 9 – 15 + 6 = 0. The Factor Theorem extends this, indicating if f(a) = 0, then (x – a) is a factor of the polynomial. These shortcuts alleviate long division and facilitate polynomial factoring, essential in solving polynomial equations, analyzing algebraic structures, and simplifying advanced math problems with speed and precision.
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