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Factoring Trinomials: Methods and Examples

Learn how to factor trinomials using various methods, such as the area model and grouping, with detailed examples provided for better understanding. Discover common factors, rewrite terms, and solve equations efficiently.

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Factoring Trinomials: Methods and Examples

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  1. Chapter 5 Section 4 Factoring Trinomials

  2. Findtwonumbers • Sum is 11, product is 24 • Sum is -14, product is 40 • Sum is 10, product is -24 • Sum is -7, product is -30

  3. What is the sum and product?

  4. Area Model Factor: Sum is 11, product is 24. Two numbers are: 8 and 3 Make a box with 4 square inside.

  5. Area Model • Factor: 2x2 8x • 3x 12 • Find the common factors and write on top and on the left side.

  6. Factor 2x2 + 11x+12 x 4 2x 2x2 8x 3 3x 12 Answer: (x + 4)(2x + 3)

  7. Factor 2x2 + 11x+12 • Grouping • Sum is 11, product is 24 • Two number are 3 and 8 • Rewrite the middle (linear) term using the two numbers. • 2x2 + 3x + 8x +12 • Factor by groups.

  8. Continue • 2x2 + 3x + 8x +12 • Factor by groups • (2x2 + 3x) + (8x +12) • Common factor • x(2x + 3) + 4(2x + 3) • (2x + 3)(x + 4)

  9. Try • Factor: 3x2 + 8x + 5

  10. Look at this • Factor: 3x2 + 3x – 18 • Note: Find the common factor first.

  11. On paper • Factor: 3x2 + 3x – 18

  12. Factor e) f) g)

  13. Factor h) i) j)

  14. Summary • Found two numbers that were the sum and product. • Factored a trinomial • Area model • grouping

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