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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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