Dividing x³ - 2x² - 5x + 6 by (x - 3)

Algebra 2 · Axiom Academy

EXAMPLE Dividing x^3 - 2x^2 - 5x + 6 by (x - 3) Work through polynomial long division step by step, then verify the result two independent ways. Divide x^3 - 2x^2 - 5x + 6 by (x - 3) using polynomial long division. Great work — you've completed polynomial long division from start to finish. Here's the pattern, plus two independent checks that confirm the answer is right. Divide, Multiply, Subtract, Bring Down: this four-step cycle repeats until every term has been brought down. Always divide the leading terms: the highest-degree term of the current working polynomial determines the next quotient term. Watch your signs: subtracting a polynomial means flipping the sign of every term inside it — this is where most long-division mistakes happen. Check 1 — multiply back: (x-3)(x^2+x-2) = x^3-2x^2-5x+6 , exactly the original dividend. Check 2 — Remainder Theorem: P(3) = 27-18-15+6 = 0 , matching the remainder we found by division. Since the remainder is 0 , (x-3) is a factor of x^3-2x^2-5x+6 — and the polynomial factors completely as (x-3)(x+2)(x-1) .

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