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ALG2.111 Writing Polynomials from Zeros Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.111 Writing Polynomials from Zeros. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.111 Writing Polynomials from Zeros - Practice questions for Writing Polynomials from Zeros.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.111 Writing Polynomials from Zeros skill assessments:

Problem 1Difficulty: Mastery

Minimal degree, real coefficients. A polynomial with real coefficients has nonreal zero(s) 0+3i, 3+1i (mult. 2) (and each conjugate). The leading coefficient is -3. Which function matches?

Af(x) = -3(x²+9)(x²-6x+10)²

Bf(x) = -3(x²+9)²(x²-6x+10)²

Cf(x) = 3(x²+9)(x²-6x+10)²

Df(x) = -3(x²+9)(x²-6x+8)²

Solution & Explanation:Write a factor for each zero: (x-r) raised to its multiplicity. A zero of 0 gives a factor x. Because the coefficients are real, each nonreal zero a+bi requires its conjugate a-bi. Together they make a real quadratic factor x²-2ax+(a²+b²). Multiply the product of factors by the leading coefficient -3.

Problem 2Difficulty: Mastery

A polynomial has zeros 6, 2 (mult. 2), -2. It also satisfies f(1) = -15. Which function is correct?

Af(x) = 2(x-6)(x-2)²(x+2)

Bf(x) = (x-6)(x-2)²(x+2)

Cf(x) = -(x-6)(x-2)²(x+2)

Df(x) = 3(x-6)(x-2)²(x+2)

Solution & Explanation:First write g(x) as the product of factors from the zeros (include conjugates for nonreal zeros). Then f(x)=a·g(x). Use the point (1,-15): a = -15/g(1).

Problem 3Difficulty: Mastery

A polynomial has zeros 3, 0, -2 (mult. 2). It also satisfies f(2) = 64. Which function is correct?

Af(x) = 2(x-3)x(x+2)²

Bf(x) = -2(x-3)x(x+2)²

Cf(x) = -3(x-3)x(x+2)²

Df(x) = -(x-3)x(x+2)²

Solution & Explanation:First write g(x) as the product of factors from the zeros (include conjugates for nonreal zeros). Then f(x)=a·g(x). Use the point (2,64): a = 64/g(2).

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard ALG2.111 (Practice questions for Writing Polynomials from Zeros.).