Divide polynomials using long division

Learning Objectives Correctly set up a polynomial long division problem, including the use of placeholders for missing terms. Execute the iterative 'Divide, Multiply, Subtract, Bring Down' algorithm for polynomials. Identify the quotient and remainder from the result of polynomial long division. Express the solution of a polynomial division in the form P(x) = D(x)Q(x) + R(x). Verify the result of a polynomial division problem through multiplication and addition. Determine if a binomial is a factor of a polynomial by checking for a zero remainder. You know how to divide 125 by 5, but how would you divide (x³ + 8) by (x + 2)? 🤔 Let's explore the algebraic equivalent of a fundamental arithmetic skill! This tutorial will guide you through the step-by-step proces...

TermDefinitionExample DividendThe polynomial that is being divided. It is placed inside the long division symbol.In (x² + 5x + 6) ÷ (x + 2), the dividend is x² + 5x + 6. DivisorThe polynomial by which the dividend is being divided. It is placed outside the long division symbol.In (x² + 5x + 6) ÷ (x + 2), the divisor is x + 2. QuotientThe main result of the division. It is written on top of the long division symbol.In (x² + 5x + 6) ÷ (x + 2), the quotient is x + 3. RemainderThe polynomial 'left over' after the division is complete. The division is exact if the remainder is 0.In (x² + 5x + 7) ÷ (x + 2), the remainder is 1. Degree of a PolynomialThe highest exponent of the variable in a polynomial.The degree of 3x⁴ - 2x + 1 is 4. Placeholder TermA term with a coefficient of 0 used...

The Division Algorithm for Polynomials P(x) = D(x)Q(x) + R(x) This rule states that the Dividend (P(x)) is equal to the Divisor (D(x)) multiplied by the Quotient (Q(x)), plus the Remainder (R(x)). This is used to write the final answer and to verify it. Fractional Form of the Result \frac{P(x)}{D(x)} = Q(x) + \frac{R(x)}{D(x)} This is an alternative way to express the result of the division, which is particularly useful when working with rational functions. The degree of R(x) must be less than the degree of D(x).