MAT-HS Targeted Standards (A) Concept: Algebra (SSE) Domain: Arithmetic with Polynomials and Rational Expressions Cluster: Perform arithmetic operations on polynomials

MAT-HS.A-APR.02 Apply the Remainder Theorem.

Student Learning Targets:

Knowledge Targets

I can use the fact that a is a zero of a polynomial.

Reasoning Targets

I can

I can

Skills (Performance) Targets

I can apply the Remainder Theorem to a polynomial.

Product Targets

I can

I can

Alg II Solve Polynomial Equations Proficiency Scale

Score

Description

Sample Activity

4.0

(advanced)

In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.

Describe and correct the error in using synthetic division to divide x^{3}-5x+3 by x-2.

3.5

In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

The student can:

use and apply the remainder theorem/synthetic division to find the zeros of a polynomial function, real and imaginary.

use and apply long division/synthetic division to find the zeros of a polynomial function.

The student exhibits no major errors or omissions.

Find the zeros:

f(x)= x^{3}-10x^{2}+19x+30

f(x)=2x^{5}+3x^{4}-30x^{3}-57x^{2}-2x+24

f(x)=x^{3}-4x^{2}+25x-100

2.5

The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

There are no major errors or omissions regarding the simpler details and processes as the student can:

recognize and recalls specific terminology, such as:

factors

zeros

imaginary/complex numbers

synthetic division or long division

fundamental theorem of Algebra

possible zeros (p/q)

solve simple quadratic equations.

use synthetic division to divide polynomials.

can perform operations with complex numbers.

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Synthetically divide to find the remaining zeros.

(6x^{3}-19x^{2}+16x-4)(x-2)

(2x^{4}+7x^{3}-4x^{2}-27x-18)(x+3)

1.5

The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).

0.5

With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).

0.0

Even with help, the student demonstrates no understanding or skill.