Georgia Milestones Algebra II Arithmetic with Polynomials and Rational Expressions. Practice it free.

Students perform arithmetic operations and understand polynomial and rational relationships. This Algebra II reporting domain maps to 7 practice skills and 8 representative questions from the playable bank.

Algebra II7 mapped skills
What the test measures

Arithmetic with Polynomials and Rational Expressions skills

  1. Perform arithmetic operations with polynomials

  2. Understand the relationship between zeros and factors of polynomials

  3. Use polynomial identities to solve problems

  4. Rewrite rational expressions

Standards basis

Georgia Standards of Excellence (state-adopted content standards) — Georgia

How the Georgia Milestones reports it

Georgia Milestones is Georgia’s own statewide assessment system, aligned to Georgia’s state-adopted content standards rather than a shared national test framework. The official page says it measures knowledge and skills in the state-adopted standards for mathematics across grades 3 through high school ([Georgia Department of Education](https://gadoe.org/assessment-accountability/georgia-milestones/)).

Blueprint & weighting

Not published on the official Georgia Milestones overview page reviewed here.

Practice by skill

Topics mapped to this domain

Binomial theorem and factorials

Grade 1115 questions

Factorable polynomial zeros (ACT)

Grade 910 questions

Monomial expression multiplication (SAT)

Grade 920 questions

Polynomial combining like terms (ACT/SAT)

Grade 910 questions

Polynomial expression multiplication (SAT)

Grade 910 questions

Simplifying rational expressions (ACT)

Grade 910 questions

Square and cube binomials

Grade 910 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

What is C(5,3)C(5, 3)?

C(5,3)=5!3! (5−3)!=10C(5,3) = \dfrac{5!}{3!\,(5-3)!} = 10.

Practice playeasy

What are all and only the zeros of the polynomial defined by p(x)=x2+x−12p(x)=x^2+x-12?

Factor: x2+x−12=(x+4)(x−3)x^2+x-12=(x+4)(x-3). After factoring, set each linear factor equal to zero: (x+4)=0⇒x=−4(x+4)=0 \Rightarrow x=-4; (x−3)=0⇒x=3(x-3)=0 \Rightarrow x=3. The zeros are −4-4 and 33.

Practice playeasy

Which expression is equivalent to (5x)(3x)?(5x)(3x)\textsf{?}

Multiply the coefficients: 5⋅3=15.5 \cdot 3 = 15\textsf{.} Add the exponents on xx: x1+1=x2.x^{1+1} = x^{2}\textsf{.} So the product is 15x2.15x^{2}\textsf{.}

Practice playmedium

Simplify: (7x2+2x−3)−(5x2−2x+1).(7x^2 + 2x - 3) - (5x^2 - 2x + 1)\textsf{.}

Distribute the minus sign: (7x2+2x−3)−5x2+2x−1.(7x^2 + 2x - 3) - 5x^2 + 2x - 1\textsf{.} Combine x2x^2 terms: 7x2−5x2=2x2.7x^2 - 5x^2 = 2x^2\textsf{.} Combine xx terms: 2x+2x=4x.2x + 2x = 4x\textsf{.} Combine constants: −3−1=−4.-3 - 1 = -4\textsf{.} Result: 2x2+4x−4.2x^2 + 4x - 4\textsf{.}

Practice playmedium

Which expression is equivalent to (x−2)(x+7)−5(x - 2)(x + 7) - 5?

Expand: (x−2)(x+7)=x2+7x−2x−14=x2+5x−14(x - 2)(x + 7) = x^2 + 7x - 2x - 14 = x^2 + 5x - 14. Then subtract 55: x2+5x−14−5=x2+5x−19x^2 + 5x - 14 - 5 = x^2 + 5x - 19.

Practice playmedium

Which expression is equivalent to x3−8x2−4\dfrac{x^{3}-8}{x^{2}-4} when x≠2x \neq 2 and x≠−2?x \neq -2\textsf{?}

Factor: (x−2)(x2+2x+4)(x−2)(x+2)=x2+2x+4x+2\dfrac{(x-2)(x^{2}+2x+4)}{(x-2)(x+2)}=\dfrac{x^{2}+2x+4}{x+2} for x≠±2.x \neq \pm 2\textsf{.}

Practice playeasy

Which expression is equivalent to (x+5)2(x + 5)^{2}?

(x+5)2=x2+2(x)(5)+52=x2+10x+25(x + 5)^{2} = x^{2} + 2(x)(5) + 5^{2} = x^{2} + 10x + 25.

Practice playeasy

What is 6!6!?

6!=6×5×4×3×2×1=7206! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720.

Keep practicing

Turn arithmetic with polynomials and rational expressions into game time.

The Georgia Milestones placement starts with this test's real coverage map and finds the right difficulty.

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Related Common Core standards
HSA.APR.C.5HSA.APR.A.1
Arithmetic with Polynomials and Rational Expressions in other Georgia Milestones grades
Algebra I
The same skills on other tests
NJSLAPARCC
Source and test overview
All Georgia Milestones prepOfficial test source
Reporting categories

More Algebra II domains

The Complex Number SystemStudents perform arithmetic operations with complex numbers and use them in polynomial identities and equations.8 QsPractice →Seeing Structure in ExpressionsStudents interpret and rewrite expressions to reveal structure and create equivalent forms.8 QsPractice →Creating EquationsStudents create equations and inequalities that model relationships.8 QsPractice →Reasoning with Equations and InequalitiesStudents solve equations and inequalities and analyze systems and algebraic structure.8 QsPractice →Interpreting FunctionsStudents analyze functions and use function notation in context and by representation.8 QsPractice →Building FunctionsStudents build and compare functions that model relationships.8 QsPractice →