GED® Algebra: Expressions and Polynomials
A GED® Mathematical Reasoning bridge course for algebraic expressions, properties, substitution, equivalent forms, exponent rules, polynomials, factoring, and rational expressions. Students build the symbolic fluency needed before equations, inequalities, functions, and advanced algebra.
📚 Course Curriculum
Algebra begins with expressions. An expression is a mathematical phrase without an equals sign, such as:. An expression can be simplified or evaluated, but it …
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The GED® often asks you to turn a situation into an algebraic expression. Translation is not about memorizing one keyword; it is about preserving meaning …
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To evaluate an expression, replace the variable with a specific number and simplify. Substitution must be careful, especially for negative numbers. Example:. Replace \(x\) with …
Open trial session →Like terms have exactly the same variable part. You may combine their coefficients because they count the same kind of object. Examples:. But \(3x+5\) cannot …
Open trial session →The distributive property says:. A number or expression outside parentheses multiplies every term inside. [[figure:distributive_area_model The area model shows why \(4(x+3)\) becomes \(4x+12\).]]. Examples:. The …
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Two expressions are equivalent if they have the same value for every allowed value of the variable. For example:. are equivalent. The algebraic properties explain …
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Factoring rewrites an expression as multiplication. It is the reverse of distributing. The first factoring move is usually to pull out the greatest common factor …
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Exponent rules are shortcuts for repeated multiplication. They work only when the bases are handled correctly. Product rule:. You add exponents because the repeated factors …
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A polynomial is a sum or difference of terms with whole-number exponents on variables:. [[figure:polynomial_degree The degree of a polynomial is the highest exponent among …
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Adding and subtracting polynomials is combining like terms. Example:. Combine like terms:. Subtraction requires distributing the negative sign:. Rewrite:. Then combine:. To multiply a monomial …
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Factoring a trinomial reverses binomial multiplication. [[figure:factoring_trinomial For \(x^2+5x+6\), find two numbers that multiply to 6 and add to 5.]]. For:. find two numbers that …
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A rational expression is a fraction whose numerator or denominator contains a variable, such as:. [[figure:rational_expression_restriction A rational expression is undefined when its original denominator …
Open trial session →Course Syllabus
This self-paced GED® Math course follows a 12-lesson sequence. Work through the modules in order so that each skill supports the next.
Course sequence
Module 1 - Lessons 1-4
- Variables, Terms, Coefficients, and Constants
- Translating Words and Contexts into Expressions
- Evaluating Expressions by Substitution
- Combining Like Terms
Module 2 - Lessons 5-8
- The Distributive Property and Negative Groups
- Algebraic Properties and Equivalent Expressions
- Factoring Out the Greatest Common Factor
- Exponent Rules for Algebra
Module 3 - Lessons 9-12
- Polynomial Degree and Standard Form
- Adding, Subtracting, and Multiplying Polynomials
- Factoring Trinomials and Special Products
- Rational Expressions, Restrictions, and GED® Modeling
Practice and completion
- Use worked examples and lesson practice to check understanding after each module.
- Review incorrect answers, explain the correction, and repeat weak skills.
- Complete the available mixed or final course practice to demonstrate readiness.
Course Outcomes
By the end of this course, learners will be able to:
- Explain and apply the mathematical ideas in Variables, Terms, Coefficients, and Constants.
- Solve multi-step problems involving Combining Like Terms and show a clear method.
- Interpret representations and check the reasonableness of work involving Factoring Out the Greatest Common Factor.
- Choose efficient strategies for unfamiliar questions related to Polynomial Degree and Standard Form.
- Combine skills from Rational Expressions, Restrictions, and GED® Modeling with earlier topics in mixed practice.
- Use feedback and answer explanations to diagnose and correct mistakes.
- Complete mixed, exam-style practice with clearer reasoning and greater independence.
📝 Practice Questions
52 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.