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Factoring Foundations

A free Algebra I lesson from the “Exponents and Polynomials” unit, with a worked example and practice problems including step-by-step solutions.

Factoring rewrites a polynomial as a product. Start by checking for a greatest common factor, then look for patterns such as difference of squares or trinomials. In Exponents and Polynomials, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.

What you'll learn

Why it matters: Factoring reveals hidden structure in area expressions, break-even equations, and formulas that need to be solved in pieces.

Worked example

Problem. Factor 6x + 18.

  1. Find the greatest common factor of 6x and 18.
  2. The GCF is 6.
  3. Factor 6 out of each term: 6(x + 3).
  4. Connect the result back to Factoring Foundations so the method and meaning are both clear.

Answer: 6(x + 3)

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.

Practice problems

1. Factor 4x + 12.

Choices: 4(x + 3) · 4x(12) · x(4 + 12) · 2(2x + 12)

Show solution
  1. The greatest common factor is 4.

Answer: 4(x + 3)

2. Factor 3x^2 + 6x.

Choices: 3x(x + 2) · 3(x^2 + 6x) · x(3x + 6x) · 6x(3x + 1)

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  1. Both terms share 3x.

Answer: 3x(x + 2)

3. Which is a difference of squares?

Choices: x^2 - 25 · x^2 + 25 · x^2 - 5x · x^2 + 10x + 25

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  1. It is x^2 minus 5^2.

Answer: x^2 - 25

4. Factor x^2 - 16.

Choices: (x - 4)(x + 4) · (x - 8)(x + 2) · (x + 4)(x + 4) · (x - 4)(x - 4)

Show solution
  1. Difference of squares: x^2 - 4^2.

Answer: (x - 4)(x + 4)

5. Factor x^2 + 7x + 12.

Choices: (x + 3)(x + 4) · (x + 2)(x + 6) · (x - 3)(x - 4) · (x + 1)(x + 12)

Show solution
  1. 3 and 4 multiply to 12 and add to 7.

Answer: (x + 3)(x + 4)

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