Division with decimal quotients

Learning Objectives Perform long division with whole numbers to produce a decimal quotient. Set up a polynomial long division problem correctly, including placeholders for missing terms. Apply the division algorithm (Divide, Multiply, Subtract, Bring Down) to divide a polynomial by a binomial. Identify the polynomial quotient and the remainder from the division process. Express the result of polynomial division as a mixed rational expression in the form Q(x) + R(x)/D(x). Substitute a given value for the variable to evaluate the rational expression and find a final decimal quotient. Ever wonder how a GPS calculates the exact time to a destination, even with fractional minutes? It involves precise division! 🗺️ This tutorial connects the long division you already know with pol...

TermDefinitionExample Rational ExpressionA fraction where both the numerator (top) and the denominator (bottom) are polynomials. The denominator cannot be zero.(x^2 + 2x + 1) / (x - 3) DividendThe polynomial that is being divided.In (x^2 + 5x + 6) ÷ (x + 2), the dividend is x^2 + 5x + 6. DivisorThe polynomial that you are dividing by.In (x^2 + 5x + 6) ÷ (x + 2), the divisor is x + 2. QuotientThe main result of the division, before considering the remainder.In 25 ÷ 4, the quotient is 6. RemainderThe value or polynomial 'left over' after the division is complete.In 25 ÷ 4, the remainder is 1. Decimal QuotientThe complete numerical result of a division, including the fractional part expressed as a decimal.The decimal quotient of 25 ÷ 4 is 6.25.

The Division Algorithm P(x) = D(x) \cdot Q(x) + R(x) This states that any polynomial Dividend, P(x), can be rewritten as its Divisor, D(x), times its Quotient, Q(x), plus its Remainder, R(x). This is the foundation of the long division process. Rational Expression Form \frac{P(x)}{D(x)} = Q(x) + \frac{R(x)}{D(x)} This rule shows how to write a rational expression using the results of polynomial long division. To find a final decimal value, you evaluate this expression for a given value of x. Long Division Cycle 1. Divide -> 2. Multiply -> 3. Subtract -> 4. Bring Down This is the repeating four-step process used in both numerical and polynomial long division to find the quotient and remainder.