Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a polynomial division quiz? Then this Algebra 2 quiz on Dividing Polynomials: Remainder and Factor Theorems asks 10 multiple-choice questions with instant feedback.
Ten multiple-choice questions on polynomial division, the Remainder and Factor Theorems, and identities. Watch the sign of the value used in synthetic division and remember that the remainder equals the function value.
Standards: A-APR.B.2, A-APR.D.6, A-APR.C.4 · Level: Grade 11 Algebra 2
What this Dividing Polynomials: Remainder and Factor Theorems quiz checks
- f(x) = d(x)·q(x) + r(x), and the degree of r is less than the degree of d.
- Synthetic division works only for divisors of the form x − r.
- Remainder Theorem: dividing f(x) by x − r leaves the remainder f(r).
- Factor Theorem: f(r) = 0 exactly when x − r is a factor of f(x).
- Polynomial identities such as (x2 + y2)2 = (x2 − y2)2 + (2xy)2 can be proved by expanding.
The 10 questions of the quiz
- What is the remainder when x2 − 4x + 9 is divided by x − 3?
- Which value of r is used in synthetic division by x + 5?
- Which is a factor of x3 + 4x2 − 7x − 10?
- What is (x2 − x − 20) ÷ (x − 5)?
- The completed synthetic division table is shown. What is the remainder?
- If f(−3) = 0, which statement must be true?
- What is the product (6x − 11)(6x + 11)?
- The graph of f is shown. What is the remainder when f(x) is divided by x − 1?
- A degree 8 polynomial is divided by a linear factor with no remainder. What is the degree of the quotient?
- What is 1,0012 − 9992?
After the quiz
Missed a question? Reread the Dividing Polynomials: Remainder and Factor Theorems lesson, then take the quiz again. Next, solve the Algebra 2 worksheet on Dividing Polynomials: Remainder and Factor Theorems, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.