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Factoring Quadratic Trinomials

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Factoring Quadratic Trinomials

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Factoring Quadratic Trinomials

  1. 1. Grade 8 – Mathematics Quarter I FACTORING QUADRATIC TRINOMIALS of the form 𝒙 𝟐 + 𝒃𝒙 + 𝒄
  2. 2. Objectives: 1. factor quadratic trinomials of the form 𝑥2 + 𝑏𝑥 + 𝑐 ; and 2. solve problems involving factors of polynomials.
  3. 3. List all pairs of integers (factors) of the following numbers. 4 1 and 4 2 and 2 10 1 and 10 2 and 5 8 1 and 8 2 and 4 6 1 and 6 2 and 3
  4. 4. List all pairs of integers (factors) of the following numbers. 12 1 and 12 2 and 6 3 and 4 30 1 and 30 2 and 15 3 and 10 20 1 and 20 2 and 10 4 and 5 18 1 and 18 2 and 9 3 and 6
  5. 5. FACTORING. 𝒙 𝟐 + 𝒃𝒙 + 𝒄 1. List all pairs of integers (m · n) whose product is c. 2. Choose a pair whose sum (m + n) is b. 𝒙 𝟐 + 𝒃𝒙 + 𝒄 = (x + m)(x + n)
  6. 6. FACTORING. 𝒙 𝟐 + 𝒃𝒙 + 𝒄 𝒙 𝟐 + 𝒃𝒙 + 𝒄 = (x + m)(x + n) (m · n)(m + n) Factored Form
  7. 7. Example: 𝒙 𝟐 + 𝟏𝟎𝒙 + 𝟏𝟔 List all pairs of integers whose product is c. 1 and 16 2 and 8 4 and 4 Choose a pair whose sum is b. 2 and 8 = 10 Factor as (x + m)(x + n). m n 𝒙 𝟐 + 𝟏𝟎𝒙 + 𝟏𝟔 = (x + 2)(x + 8) (+)(+) (-)(-)
  8. 8. Example: 𝒙 𝟐 − 𝟗𝒙 + 𝟏𝟖 List all pairs of integers whose product is c. -1 and -18 -2 and -9 -3 and -6 Choose a pair whose sum is b. -3 and -6 = -9 Factor as (x + m)(x + n). m n 𝒙 𝟐 − 𝟗𝒙 + 𝟏𝟖 = (x - 3)(x - 6) (+)(+) (-)(-)
  9. 9. Example: 𝒙 𝟐 − 𝟐𝒙 − 𝟐𝟒 List all pairs of integers whose product is c. 1 and -24 2 and -12 4 and -6 3 and -8 Choose a pair whose sum is b. 4 and -6 = -2 Factor as (x + m)(x + n). m n 𝒙 𝟐 − 𝟐𝒙 − 𝟐𝟒 = (x + 4)(x - 6) (+) (-)larger integer
  10. 10. Example: 𝒙 𝟐 + 𝟑𝒙 − 𝟏𝟎 List all pairs of integers whose product is c. -1 and 10 -2 and 5 Choose a pair whose sum is b. -2 and 5 = 3 Factor as (x + m)(x + n). m n 𝒙 𝟐 + 𝟑𝒙 − 𝟏𝟎 = (x - 2)(x + 5) (+) (-)larger integer
  11. 11. Example: 𝒙 𝟐 + 𝟑𝒙 + 𝟑 List all pairs of integers whose product is c. 1 and 3 since 1 and 3 = 4 PRIME TRINOMIAL then 𝒙 𝟐 + 𝟑𝒙 + 𝟑 cannot be factored using integer coefficients, then it is… (+)(+) (-)(-)
  12. 12. Example: Use factoring to find the dimensions of the given box with volume represented by the expression 𝟒𝒙 𝟑 + 𝟏𝟔𝒙 𝟐 − 𝟒𝟖𝒙 The dimension of the box are 4x, x + 6 and x – 2 𝟒𝒙(𝒙 𝟐 + 𝟒𝒙 − 𝟏𝟐)Factor out 4x. 4x(x + 6)(x – 2)Factor (𝒙 𝟐 +𝟒𝒙 − 𝟏𝟐)
  13. 13. Summary. 𝒙 𝟐 + 𝟕𝒙 + 𝟏𝟎 (+)(+) or (-)(-) 𝒙 𝟐 − 𝟕𝒙 + 𝟏𝟎 (+)(+) or (-)(-) 𝒙 𝟐 + 𝟑𝒙 − 𝟏𝟎 (+) (-) 𝒙 𝟐 − 𝟑𝒙 − 𝟏𝟎 larger integer (+) (-) larger integer

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