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Factoring Trinomials

Factoring Trinomials. Lesson 29. Factoring Trinomials. Trinomial – 3 terms. When factoring a trinomial, we need to look at the second term and the third term to help find the factors . The factors of a trinomial will be two binomials. Let’s take a Look. y 2 + 3y + 2.

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Factoring Trinomials

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  1. Factoring Trinomials Lesson 29

  2. Factoring Trinomials • Trinomial – 3 terms. • When factoring a trinomial, we need to look at the second term and the third term to help find the factors. • The factors of a trinomial will be two binomials.

  3. Let’s take a Look y2 + 3y + 2 Middle Term: Sum of 3 Last Term: Product of 2 What two numbers add up to +3 ( 2 and 1 ) Same two numbers that multiply to give you +2 Factors: Options: 1 and 2 Therefore: y2 + 3y + 2 = (y + 1)(y + 2)

  4. Let’s take a Look g2 – 4g + 3 Middle Term: Sum of -4 Last Term: Product of 3 What two numbers add up to -4 Same two numbers that multiply to give you 3 Factors: Options: 1 and 3 or -1 and -3 Therefore: g2 – 4g + 3 = (g - 1)(g - 3)

  5. Let’s take a Look x2 – 7x + 12 Middle Term: Sum of -7 Last Term: Product of 12 What two numbers add up to -7 Same two numbers that multiply to give you 12 Factors: Options: 1 x 12 or -1 x -12 2 x 6 or -2 x -6 3 x 4 or -3 x -4 Which gives a sum of -7? (-3) + (-4) Therefore: x2 – 7x + 12 = (x - 4)(x - 3)

  6. Chart to Help with Signs

  7. YOU TRY! x2 + 6x + 8 Middle Term: Sum of 6 Last Term: Product of 8 What two numbers add up to + 6 Same two numbers that multiply to give you 8 Factors: Options: Which gives a sum of +6? Therefore: x2 + 6x + 8 = (x )(x )

  8. SOLUTIONS x2 + 6x + 8 Middle Term: Sum of 6 Last Term: Product of 8 What two numbers add up to + 6 Same two numbers that multiply to give you 8 Factors: Options: 1 x 8 or -1 x -8 2 x 4 or -2 x -4 Which gives a sum of +6? (2 and 4) Therefore: x2 + 6x + 8 = (x + 2)(x + 4)

  9. YOU TRY! x2 + 2x - 15 Middle Term: Sum of 2 Last Term: Product of -15 What two numbers add up to + 2 Same two numbers that multiply to give you -15 Factors: Options: Which gives a sum of +2? Therefore: x2 + 2x - 15 = (x )(x )

  10. SOLUTIONS x2 + 2x - 15 Middle Term: Sum of 2 Last Term: Product of -15 What two numbers add up to + 2 Same two numbers that multiply to give you -15 Factors: Options: 1 x 15 or -1 x -15 3 x 5 or -3 x -5 Which gives a sum of +2? -3 and +5 (use chart to help with signs) Therefore: x2 + 2x - 15 = (x -3)(x + 5)

  11. YOU TRY! y2 - 4y - 12 Middle Term: Sum of - 4 Last Term: Product of -12 What two numbers add up to - 4 Same two numbers that multiply to give you - 12 Factors: Options: Which gives a sum of - 4? Therefore: y2 – 4y - 12 = (y )(y )

  12. SOLUTIONS y2 - 4y - 12 Middle Term: Sum of - 4 Last Term: Product of -12 What two numbers add up to - 4 Same two numbers that multiply to give you - 12 Factors: Options: 1 x 12 or -1 x -12 2 x 6 or -2 x -6 3 x 4 or -3 x -4 Which gives a sum of - 4? - 6 and + 2 Therefore: y2 – 4y - 12 = (y - 6)(y + 2)

  13. YOU TRY! y2 - 5y + 4 Middle Term: Sum of - 5 Last Term: Product of + 4 What two numbers add up to - 5 Same two numbers that multiply to give you + 4 Factors: Options: Which gives a sum of - 5? Therefore: y2 – 5y + 4 = (y )(y )

  14. SOLUTIONS y2 - 5y + 4 Factors: Middle Term: Sum of - 5 Last Term: Product of + 4 What two numbers add up to - 5 Same two numbers that multiply to give you + 4 Options: 1 x 4 or -1 x -4 2 x 2 or - 2 x -2 Which gives a sum of - 5? -1 and - 4 Therefore: y2 – 5y + 4 = (y -1)(y - 4)

  15. Class work • Check solutions to Lesson 28(2) on my desk • Lesson 29 worksheet • Reminder that Solutions are are on my desk

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