22-23 - Copy.pptx
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The document discusses factoring different types of trinomials, including perfect square trinomials where the first and last terms are perfect squares and the middle term is twice the product of the first and last terms, and general trinomials where two integers are found whose product is the last term and sum is the middle term to fully factor the expression. Examples are provided of factoring perfect square and general trinomial expressions.
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- 2. FIRST TERM Perfect Square Trinomial PERFECT SQUARE LAST TERM PERFECT SQUARE MIDDLE TERM TWICE THE PRODUCT of FIRST and LAST TERM (positive) (positive) PERFECT SQUARE
- 3. Perfect Square Trinomials 𝒙𝟐 + 𝟐𝒙𝒚 + 𝒙𝟐 (𝒙)𝟐 +𝟐(𝒙)(𝒚) + (𝒚)𝟐
- 4. 𝟏. 𝒂𝟐 − 𝟐𝟐𝒂 + 𝟏𝟐𝟏 𝟐. 𝒃𝟐 − 𝟖𝒃 + 𝟏𝟔 𝟑. 𝟒𝒅𝟐 + 𝟐𝟎𝒅 − 𝟐𝟓
- 5. 𝟒. 𝟏𝟎𝟎 + 𝟓𝟎𝒆 + 𝒆𝟐 𝟓. 𝟑𝟔𝒓𝟐 − 𝟔𝟎𝒓𝒕 + 𝟐𝟓𝒕𝟐
- 6. Factoring Perfect Square Trinomials 𝒙𝟐 + 𝟐𝒙𝒚 + 𝒚𝟐 𝒙𝟐 − 𝟐𝒙𝒚 + 𝒚𝟐 = (𝒙 + 𝒚)𝟐 FIRST FIRST LAST LAST = (𝒙 − 𝒚)𝟐 FACTORED FORM
- 7. Factoring Perfect Square Trinomials 𝒙𝟐 + 𝟏𝟎𝒙 + 𝟐𝟓= (𝒙 + 𝒚)𝟐 Factor. (𝒙)𝟐 +𝟐(𝒙)(𝟓) + (𝟓)𝟐 = (𝒙 + 𝟓)𝟐 Factored Form: Check:
- 9. MODULE 1B Lesson 2 – What’s In Activity: The Two of Us
- 10. Factoring General Trinomials 𝒙𝟐 + 𝒃𝒙 + 𝒄 = (𝒙 + 𝒎)(𝒙 + 𝒏) 1. List all pairs of integers (m∙n) whose product is 𝒄. 2. Choose a pair whose sum (m+n) is 𝒃. 𝒙𝟐 + 𝒃𝒙 + 𝒄
- 11. Factoring General Trinomials 𝒙𝟐 + 𝒃𝒙 + 𝒄 = (𝒙 + 𝒎)(𝒙 + 𝒏) 𝒙𝟐 + 𝒃𝒙 + 𝒄 (m+n) (m∙n) FACTORED FORM
- 12. Factoring General Trinomials 𝒙𝟐 + 𝟏𝟎𝒙 + 𝟏𝟔 = (𝒙 + 𝒎)(𝒙 + 𝒏) 𝒙𝟐 + 𝒃𝒙 + 𝒄 Factor. (+)(+) (-)(-) 𝒙𝟐 + 𝟏𝟎𝒙 + 𝟏𝟔 2 + 8 = 10 = (𝒙 + 𝟐)(𝒙 + 𝟖) m n
- 13. Assessment: MODULE 1B Lesson 1 – What’s More Activity 1: You’re the One Lesson 2 – What’s More Activity 1: Missing You!
- 14. Study Math for a Better Path