Polynomial Long Division

Algebra 2 · Axiom Academy

LESSON Polynomial Long Division Master the step-by-step process of dividing polynomials using the same long division algorithm you already know from arithmetic. 1. Connection to Numerical Division Remember dividing ? The process for polynomials is the same : divide, multiply, subtract, bring down, repeat. Watch both divisions run side by side — every move happens at the same moment on both. The shape of every division — numbers or polynomials Start at the highest place value — or the highest degree — and move down. Only the front of each expression decides the next piece of the quotient. Multiply the whole divisor by that piece, then subtract the product away. Pull down what's left and run the same three moves again. Write the dividend (what you're dividing) inside Write the divisor (what you're dividing by) outside Make sure terms are in descending order by degree Leave space for missing degrees — a gap gets a 0 coefficient 3. Step 1: Divide Leading Terms Ask yourself: what times x gives me 2x^3 ? Everything else in the problem is irrelevant right now — watch it fade away. Write 2x^2 above the division bar, aligned with the x^2 position. 4. Step 2: Multiply and Subtract Now multiply 2x^2 by the entire divisor (x + 2) , write the product below the dividend with like terms aligned — and then subtract it away. What the subtraction bought us

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