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Factoring Trinomials

This lesson dives deep into the art of factoring trinomials, focusing on the relationship between the second and third terms to identify factors. By using practical examples, you'll learn to break down trinomials into binomials, such as factoring (y^2 + 3y + 2) into ((y + 1)(y + 2)). The lesson covers various trinomial scenarios including both positive and negative coefficients, offering invaluable tips to find the right pairs of numbers that meet both the sum and product criteria. Practice exercises are included to reinforce understanding.

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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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