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Factoring Polynomials

Ninth graders learn to factor polynomials — the reverse of multiplying — breaking expressions like x² + 5x + 6 back into their factors (x + 2)(x + 3), a key skill for solving quadratic equations.

Grade 9Polynomials55 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Factor out a GCF.
  • ✓Factor a trinomial.
  • ✓Factor a difference of squares.
  • ✓Check by multiplying.
Essential Question

Multiplying (x + 2)(x + 3) gives x² + 5x + 6. But can you run it in REVERSE — start with the polynomial and find the factors? That’s factoring.

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Match It · Interactive

Match the Factored Form

Project this and match each polynomial to its factored form — tap a polynomial, then tap its factors.

🔤 Match each polynomial to its factored formTry it
Polynomial
Factored Form
Tap a polynomial, then tap its factors!
The Lesson · Gradual Release (I Do · We Do · You Do)

55 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Multiplication in Reverse

5 min

(x+2)(x+3) = x²+5x+6 — can you go backward?

👩‍🏫 Teacher Moves

  • Show a product and its expansion.
  • Ask how to reverse it.
  • Set the goal: factoring.

🎒 Student Actions

  • See the product.
  • Reverse it.
  • Predict the idea.
2

I Do — Factoring Methods

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Factor out a GCF.
  • Factor a trinomial.
  • Factor a difference of squares.

🎒 Student Actions

  • Learn GCF.
  • Learn trinomials.
  • Learn difference of squares.
3

We Do — Match Together

13 min

Class uses Match the Factored Form.

👩‍🏫 Teacher Moves

  • Match each pair.
  • Check by multiplying.
  • Explain the method.

🎒 Student Actions

  • Match them.
  • Check them.
  • Explain it.
4

You Do — On Your Own

12 min

Students factor.

👩‍🏫 Teacher Moves

  • Factor GCFs.
  • Factor trinomials.
  • Factor differences of squares.

🎒 Student Actions

  • Factor GCFs.
  • Factor trinomials.
  • Factor others.
5

Close — Close

5 min

One polynomial.

👩‍🏫 Teacher Moves

  • Give a polynomial.
  • Factor it.
  • Hand out the exit ticket.

🎒 Student Actions

  • Factor it.
  • Check it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School Algebra).

CCSS
A-SSE.3a

Factor a quadratic expression to reveal the zeros.

CCSS
A-SSE.2

Use the structure of an expression to rewrite it.

CCSS
A-APR.1

Understand polynomials as a closed system.

CCSS
A-REI.4b

Solve quadratic equations by factoring.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Use algebra tiles.
  • Sentence frame: “___ factors into ___.”
  • Check by multiplying (FOIL).

Support & Access

IEP / 504
  • Start with GCF factoring.
  • Use algebra tiles.
  • Factor step by step.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Factor when a ≠ 1.
  • Factor by grouping.
  • Use factoring to solve equations.
Materials

What to gather

  • 📽️Projector / board
  • 🟦Algebra tiles
  • 💻Match the Factored Form
  • 🧮Calculators
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

factora part that multiplies to give a productpolynomialan expression of termstrinomiala three-term polynomialGCFgreatest common factordifference of squaresa² − b²quadratica degree-2 expressionFOILa way to multiply two binomialszeroa value that makes it 0
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Factor: x² + 6x + 8.
(x + 2)(x + 4).
QUESTION 2
Factor the difference of squares: x² − 16.
(x + 4)(x − 4).
QUESTION 3
Factor out the GCF: 3x² + 6x.
3x(x + 2).

Going deeper? Solve by factoring.

Have students factor a quadratic and then use the zero-product property to solve the equation (set each factor to 0). A printable factoring sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Factoring PolynomialsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Factoring PolynomialsQuiz
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1 / 6
Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Factoring PolynomialsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: difference of squares, factor, FOIL, GCF, polynomial, quadratic, trinomial, zero
  1. a value that makes it 0
  2. a three-term polynomial
  3. a² − b²
  4. a part that multiplies to give a product
  5. an expression of terms
  6. a degree-2 expression
  7. greatest common factor
  8. a way to multiply two binomials

Part B · Show what you learned

  1. Factor: x² + 6x + 8.
  2. Factor the difference of squares: x² − 16.
  3. Factor out the GCF: 3x² + 6x.
Answer key — Part A: 1) zero · 2) trinomial · 3) difference of squares · 4) factor · 5) polynomial · 6) quadratic · 7) GCF · 8) FOIL
Part B: 1) (x + 2)(x + 4). 2) (x + 4)(x − 4). 3) 3x(x + 2).