Using Synthetic Division

Pre-Calculus · Axiom Academy

EXAMPLE Using Synthetic Division Divide a polynomial by a linear factor the fast way Use synthetic division to divide , then read off the quotient and the remainder. Nice work. You ran a full synthetic division of 2x^3 - 5x^2 + 3x - 7 by (x - 2) — bring down, multiply, add, repeat. Flip the sign: dividing by (x - c) means you use +c in the box, so (x - 2) uses 2 . Bring down, then loop: multiply the latest bottom-row number by the divisor value, add into the next coefficient, and repeat. Read the bottom row: the last number is the remainder; everything before it is the quotient, dropped one degree. A nonzero remainder ( -5 ) tells you (x - 2) is not a factor — and by the Remainder Theorem it also means p(2) = -5 .

This is the written version of the interactive lesson above. See the full Pre-Calculus course.