ALGEBRA 2 HONORS - UNIT 9 (6.1 TO 6.6) PRACTICE TEST - Practice Test

Sep 30, 2026

Uploaded by Stanford

Algebra 2 Honors Unit 9 practice test covering sections 6.1 through 6.6. Students classify polynomial models, use graphing calculators to select the best-fitting model, determine relative extrema and zeros, and write polynomials from zeros or linear factors. The test includes factoring, finding zeros and multiplicities, and dividing polynomials using both long division and synthetic division, plus solving polynomial equations. It also requires rational root finding, determining complex roots, and verifying results using polynomial theorems.

LanguageEnglish

CategoryExam

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Practice Test Instructions

Answer Section: Short Answer

Polynomial functions and linear factors (6-1 to 6-2)

Dividing polynomials and solving equations (6-3 to 6-4)

Theorems about roots and fundamental theorem (6-5 to 6-6)

Name: Class: Date: ALGEBRA 2 HONORS--UNIT 9 (6.1 TO 6.6) PRACTICE TEST. GLUE IN AND SHOW ALL WORK AND EXPLAIN IN WORDS HOW TO DO EACH PROBLEM AND GET AN EXTRA CREDIT STAMP IN YOU NOTEBOOK. 1. Classify –7x5 – 6x4 + 4x3 by degree and by number of terms. 2. Use a graphing calculator to determine which type of model best fits the values in the table. | x | –6 | –2 | 0 | 2 | 6 | | --- | --- | --- | --- | --- | --- | | y | –6 | –2 | 0 | 2 | 6 | 3. Write 4x3 + 8x2 – 96x in factored form. 4. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of y = 3x3 + 15x2 − 12x − 60. If necessary, round to the nearest hundredth. 5. Find the zeros of y = x(x − 3)(x − 2) . Then graph the equation. 6. Write a polynomial function in standard form with zeros at 5,–4, and 1. 7. Find the zeros of f(x) = (x + 3) 2 (x − 5) 6 and state the multiplicity. 8. Divide 3x3 − 3x2 − 4x + 3 by x + 3. Divide using synthetic division. 9. (x4 + 15x3 − 77x2 + 13x − 36) ÷ (x − 4) 10. (x3 + 4 − 11x + 3x2 ) ÷ (x + 6) 11. Use synthetic division to find P(2) for P(x) = x4 + 3x3 − 6x2 − 10x + 8. Solve the equation by graphing. 12. x 2 + 7x + 19 = 0 13. −8x3 − 13x2 + 6x = 0 Factor the expression. 14. x 3 + 216 15. x4 − 20x2 + 64 16. Solve 125x3 + 343 = 0. Find all complex roots. 17. Solve x4 − 34x2 = −225. 18. Find the rational roots of x4 + 8x3 + 7x2 − 40x − 60 = 0. Find the roots of the polynomial equation. 19. x 3 − 2x2 + 10x + 136 = 0 20. 2x3 + 2x2 − 19x + 20 = 0 21. x4 − 5x3 + 11x2 − 25x + 30 = 0 22. A polynomial equation with rational coefficients has the roots 5 + 1 , 4 − 7 . Find two additional roots. 23. Find a third-degree polynomial equation with rational coefficients that has roots –5 and 6 + i. 24. Find a quadratic equation with roots –1 + 4i and –1 – 4i. 25. Find all zeros of 2x4 − 5x3 + 53x2 − 125x + 75 = 0. ID: A ALGEBRA 2 HONORS--UNIT 9 (6.1 TO 6.6) PRACTICE TEST. GLUE IN AND SHOW ALL WORK AND EXPLAIN IN WORDS HOW TO DO EACH PROBLEM AND GET AN EXTRA CREDIT STAMP IN YOU NOTEBOOK. Answer Section SHORT ANSWER 1. ANS: quintic trinomial REF: 6-1 Polynomial Functions 2. ANS: linear model REF: 6-1 Polynomial Functions 3. ANS: 4x(x – 4)(x + 6) REF: 6-2 Polynomials and Linear Factors 4. ANS: relative minimum: –62.24, relative maximum: 37.79, zeros: x = –5,–2, 2 REF: 6-2 Polynomials and Linear Factors 5. ANS: 0, 3, 2 REF: 6-2 Polynomials and Linear Factors 6. ANS: f(x) = x 3 − 2x2 − 19x + 20 REF: 6-2 Polynomials and Linear Factors ID: A 7. ANS: –3, multiplicity 2; 5, multiplicity 6 REF: 6-2 Polynomials and Linear Factors 8. ANS: 3x2 − 12x + 32+ –93/(x+ 3) REF: 6-3 Dividing Polynomials 9. ANS: x 3 + 19x2 − x + 9 REF: 6-3 Dividing Polynomials 10. ANS: x 2 − 3x + 7 –38/(x+6) REF: 6-3 Dividing Polynomials 11. ANS: 4 REF: 6-3 Dividing Polynomials 12. ANS: no solution REF: 6-4 Solving Polynomial Equations 13. ANS: 0,–2, 0.38 REF: 6-4 Solving Polynomial Equations 14. ANS: (x + 6)(x2 − 6x + 36) REF: 6-4 Solving Polynomial Equations 15. ANS: (x − 2)(x + 2)(x − 4)(x + 4) REF: 6-4 Solving Polynomial Equations 16. ANS: − 7 35 − 35i 3 35 + 35i 3 5 , 50 50 , 50 50 REF: 6-4 Solving Polynomial Equations 17. ANS: 3,–3, 5,–5 REF: 6-4 Solving Polynomial Equations ID: A 18. ANS: –6,–2 REF: 6-5 Theorems About Roots of Polynomial Equations 19. ANS: 3-5i,3+5i,–4 REF: 6-5 Theorems About Roots of Polynomial Equations 20. ANS: 3 + i 3 − i, , − 4 2 2 REF: 6-5 Theorems About Roots of Polynomial Equations 21. ANS: 2, 3, i 5 , −i 5 REF: 6-5 Theorems About Roots of Polynomial Equations 22. ANS: 5 − 1 , 4 + 7 REF: 6-5 Theorems About Roots of Polynomial Equations 23. ANS: x 3 − 7x2 − 23x + 185 = 0 REF: 6-5 Theorems About Roots of Polynomial Equations 24. ANS: x 2 + 2x + 17 = 0 REF: 6-5 Theorems About Roots of Polynomial Equatio

FAQs

What topics does this Algebra 2 Honors Unit 9 practice test cover?

It covers polynomial functions (6.1), polynomials and linear factors (6.2), dividing polynomials (6.3), solving polynomial equations (6.4), theorems about roots (6.5), and the fundamental theorem of algebra (6.6).

How do you handle problems that require graphing calculator results?

Use a graphing calculator to determine which model best fits table values and to find relative minima, relative maxima, and zeros for the given function, rounding if needed.

What division methods are included in the practice test?

It includes dividing polynomials using long division and synthetic division, such as dividing by linear factors and using synthetic division to evaluate P(2).

Sep 30, 2026

Uploaded by Stanford