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Algebra 1 8-6 Complete Lesson: Factoring ax² + bx+ c

By Matt Richardson
Last updated almost 3 years ago
23 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! An array of three rectangular solar panels has the area below:
The height of the array is x + 3. What is the length of the array?

Problem 1 Got It? Drag two binomial factors to the trinomial to represent its factored form.

  • (3x + 1)
  • (3x + 5)
  • (2x + 1)
  • (3x + 2)
  • 6x² + 13x + 5

Problem 1 Got It? Reasoning: Consider the trinomial below.
Suppose ac is positive and b is negative. What do you know about the factors of ac?

Problem 2 Got It?

Problem 3 Got It?

Problem 4 Got It?

Reasoning: Explain why you cannot factor the trinomial.

Reasoning: To factor the trinomial 8x² + bx + 3, a student correctly rewrites the trinomial as 8x² + px + qx + 3.

What is the value of pq? Enter only a number.

Review Lesson 8-5: Identify the factored form of each expression. Check your answer.

  • (t + 4)(t + 11)
  • (t - 5)(t - 12)
  • (t - 4)(t + 7)

Review Lesson 2-7: Match each proportion with its solution.

  • 21
  • 12.5
  • 12

Review Lesson 8-4: Simplify the product.

Review Lesson 8-4: Simplify the product.

Review Lesson 8-4: Simplify the product.

Review Lesson 8-4: Simplify the product.

Vocabulary Review: Complete each sentence with the correct form of the word factor.

  • factoring
  • factor
  • factored
  • The monomials 12x, 3x², and 6x³ have a common __?__ of 3x.
  • When __?__ a trinomial, begin by looking for a factor common to all three terms.
  • A student __?__ the expression 12x³ - 6x² into 6x²(2x - 1).

Use Your Vocabulary: You can rewrite the expression below in order to factor it.
Which rewritten expression below is NOT equivalent to the original expression?

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success