This algebra 2 polynomial division quiz asks 10 multiple-choice questions on polynomial division and the remainder theorem, and each answer comes with a short explanation.
Answer these 10 multiple-choice questions on polynomial division, the Remainder Theorem, the Factor Theorem, and polynomial identities. Each question has exactly one correct answer, and the explanation after each answer shows the key step.
The table shows synthetic division of \(x^{3}-4x^{2}+3x-5\) by \(x-2\). What is the remainder?
What is the remainder when \(x^{3}-2x^{2}+x-5\) is divided by \(x-3\)?
What is the quotient when \(x^{2}+x-12\) is divided by \(x-3\)?
If \(p(5)=0\) for a polynomial \(p(x)\), which statement must be true?
A polynomial of degree \(5\) is divided by a polynomial of degree \(2\). What is the degree of the quotient?
The graph of a cubic polynomial \(f\) crosses the x-axis at \(-3\), \(1\), and \(2\). Which is a factor of \(f(x)\)?
A right triangle has legs \(2xy\) and \(x^{2}-y^{2}\). For \(x=3\) and \(y=1\) the legs are \(6\) and \(8\). Which expression gives the hypotenuse, and what is its length?
What is the remainder when \(x^{3}+1\) is divided by \(x+1\)?
What is \((x^{3}-8)\div(x-2)\)?
Which expression is equal to \((x^{2}-y^{2})^{2}+(2xy)^{2}\) for all \(x\) and \(y\)?
🎉 Quiz complete!
How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
- Standards A-APR.B.2, A-APR.D.6, and A-APR.C.4: remainders, division of polynomials, and polynomial identities.
- Division statement: \(p(x)=d(x)q(x)+r(x)\) where the remainder has smaller degree than the divisor.
- Remainder Theorem: dividing \(p(x)\) by \(x-c\) leaves remainder \(p(c)\).
- Factor Theorem: \(x-c\) is a factor of \(p(x)\) if and only if \(p(c)=0\).
- Identity: \((x^{2}+y^{2})^{2}=(x^{2}-y^{2})^{2}+(2xy)^{2}\) generates Pythagorean triples.
How to use this algebra 2 polynomial division quiz
Retake this algebra 2 polynomial division quiz until every answer is right, then move on to the worksheet and the test.
See every chapter on the Algebra 2 math page.
