Long Division
About This Worksheet
This worksheet helps eleventh-grade Algebra 2 students practice dividing one polynomial by another using polynomial long division. Students work through five problems where a larger polynomial is divided by a binomial. They organize the work step by step, divide the leading terms, multiply back, subtract, and repeat until they reach the final quotient and remainder.
The problems are set up so students must pay attention to missing powers as well as the order of the terms. If a polynomial skips a power, students may need to leave a placeholder in their setup so everything stays lined up correctly. That organization is a big part of getting long division right.
What Students Practice
Students practice comparing the leading term of the dividend with the leading term of the divisor to decide what belongs next in the quotient. They then multiply that new term by the divisor, subtract the result, and bring down the next term.
The worksheet also gives students practice checking for a remainder. If the final result does not divide evenly, students write the leftover expression as the remainder. This helps them understand that polynomial division can work much like ordinary long division with numbers.
Why This Skill Matters
Polynomial long division is an important Algebra 2 skill because it helps students simplify higher-degree expressions and prepare for topics involving factors, zeros, and rational expressions. It also gives students a systematic method for dividing when simple factoring is not enough.
This skill becomes especially useful when students begin studying polynomial functions. Dividing by a known factor can help reveal a smaller polynomial that is easier to solve or analyze.
Common Challenges
Students may forget to write a zero term when a power is missing. For example, if there is no squared term, leaving a blank space can cause the subtraction to become misaligned. Encourage students to use placeholders so each degree stays in the correct column.
Another common mistake is subtracting only the first term after multiplying back. The entire polynomial product must be subtracted. Students should change every sign in that row before combining.
How To Use It
Teachers can use this worksheet after students understand polynomial multiplication and monomial division. It works well for guided instruction, independent practice, homework, or review before synthetic division. Modeling one full problem from start to finish can help students see the repeating pattern.
Parents and homeschool teachers can remind students that the process repeats the same four ideas: divide, multiply, subtract, bring down. Following that order slowly makes long division much easier to manage.
Grade Alignment
This worksheet is designed for Grade 11 Algebra 2 and supports polynomial arithmetic and division, especially work connected with CCSS HSA-APR.B.6, which asks students to rewrite rational expressions using polynomial division.
Students should already understand polynomial multiplication, subtraction, and exponent rules. After this practice, they are better prepared for synthetic division and factor-based polynomial work.