Polynomial Roots Practice Test

About This Polynomial Roots Practice Test

This practice test focuses on finding and interpreting polynomial zeros. The set moves beyond basic quadratic factoring to include repeated roots, cubic factorizations, complex solutions, rational-root candidates, and the relationship between zeros and linear factors.

Several questions also test multiplicity, graph behavior at intercepts, Vieta’s formulas, and the construction of a polynomial from a given set of roots.

Skills Covered

Factoring polynomials, applying the zero-product property, using the Factor and Remainder Theorems, finding sums and products of roots, recognizing complex roots, and interpreting multiplicity.

Key Ideas

1. A root r corresponds to a factor x − r.
2. Even multiplicity usually makes a graph touch the x-axis, while odd multiplicity makes it cross.
3. For ax²+bx+c, the root sum is −b/a and the product is c/a.
4. Possible rational roots come from factors of the constant divided by factors of the leading coefficient.

Common Mistakes to Avoid

Do not copy factor signs directly as roots, omit zero as a root after factoring out x, or count repeated roots as distinct roots when a question asks for distinct solutions.

Practice Format

Each explanation shows the factoring or theorem used and identifies the exact misconception represented by every distractor.