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Factor ax 2 + bx + c

Factor ax 2 + bx + c. March 31, 2014 Pages 593-596. Factors of 2. Factors of 3. Possible factorization. Middle term when multiplied. 1,2. – 1, – 3. ( x – 1)(2 x – 3). – 3 x – 2 x = – 5 x. 1 , 2. 23 , 21. ( x – 3 )( 2 x – 1 ). – x – 6 x = – 7 x. Correct.

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Factor ax 2 + bx + c

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  1. Factor ax2 + bx + c March 31, 2014 Pages 593-596

  2. Factors of 2 Factors of 3 Possible factorization Middle term when multiplied 1,2 – 1, – 3 (x – 1)(2x – 3) – 3x – 2x = – 5x 1, 2 23, 21 (x – 3)(2x– 1) – x – 6x = – 7x Correct =(x – 3)(2x – 1) ANSWER 1. Factor 2x2 – 7x + 3. When bis negative and cis positive, both factors of c must be negative. Make a table to organize your work. Check your answer using FOIL.

  3. Factors of 3 Factors of –5 Possible factorization Middle term when multiplied 1, 3 1, –5 (n + 1)(3n – 5) – 5n + 3n = – 2n 1, 3 –1, 5 (n – 1)(3n + 5) 5n – 3n = 2n 1, 3 5, – 1 (n + 5)(3n –1) – n + 15n = 14n Correct 1, 3 – 5, 1 (n – 5)(3n + 1) n – 15n = –14n = (n + 5)(3n – 1) ANSWER 2. Factor 3n2 + 14n – 5. When b is positive and cis negative, the factors ofc must have different signs.

  4. Factors of 3 Factors of 4 Possible factorization Middle term when multiplied 1, 3 1, 4 (t + 1)(3t + 4) 4t + 3t = 7t 1, 3 4, 1 (t + 4)(3t + 1) t + 12t = 13t 1, 3 2, 2 (t + 2)(3t + 2) 2t + 6t = 8t Correct = (t + 2)(3t + 2) Factor the trinomial. 3. 3t2 + 8t + 4. Because bis positive and cis positive, both factors of c are positive. Check your answer using FOIL.

  5. Factors of 4 Factors of 5 Possible factorization Middle term when multiplied 1, 4 – 1, – 5 (s – 1)(4s – 5) – 5s – 4s = – 9s 1, 4 – 5, – 1 (s – 5)(4s – 1) – s – 20s = – 21s 2, 2 – 1, – 5 (2s – 1)(2s – 5) – 10s – 2s = – 12s Correct = (s – 1)(4s – 5) 4. 4s2 – 9s + 5. Because bis negative and cis positive, both factors of c must be negative. Make a table to organize your work. Check your answer using FOIL.

  6. Factors of 2 Factors of – 7 Possible factorization Middle term when multiplied 1, 2 1, – 7 (h + 1)(2h – 7) – 7h + 2h = 5h 1, 2 – 7, 1 (h – 7)(2h + 1) h – 14h = – 13h 1, 2 – 1, 7 (h – 1)(2h + 7) 7h – 2h = 5h Correct 1, 2 7, – 1 (h + 7)(2h –1) – h + 14h = 13h = (h + 7)(2h – 1) 5.2h2 + 13h – 7. Because b is positive and cis negative, the factors ofchave different signs.

  7. 6. Factor– 4x2 + 12x + 7. SOLUTION STEP 1 Factor – 1 from each term of the trinomial. – 4x2 + 12x + 7 = –(4x2 – 12x – 7) STEP 2 Factor the trinomial 4x2 – 12x – 7. Because band care both negative, the factors of cmust have different signs. As in the previous examples, use a table to organize information about the factors of aand c.

  8. Factors of4 Factors of– 7 Possible factorization Middle term when multiplied 1, 4 1, – 7 (x + 1)(4x – 7) – 7x + 4x = – 3x 1, 4 7, – 1 (x + 7)(4x – 1) – x + 28x = 27x 1, 4 – 1, 7 (x – 1)(4x + 7) 7x – 4x = 3x 1, 4 – 7, 1 (x – 7)(4x + 1) x – 28x = – 27x 2, 2 1, – 7 (2x+ 1)(2x– 7) – 14x + 2x = – 12x Correct 2, 2 – 1, 7 (2x – 1)(2x + 7) 14x – 2x = 12x – 4x2 + 12x + 7 = –(2x + 1)(2x – 7) ANSWER

  9. ANSWER = – (y + 1)(2y + 3) Factor the trinomial. 7. – 2y2 – 5y – 3 STEP 1 Factor – 1 from each term of the trinomial. – 2y2 – 5y – 3 = –(2y2 + 5y + 3) STEP 2 Factor the trinomial 2y2 + 5y + 3. Because band care both positive, the factors of cmust have both positive. Use a table to organize information about the factors of aand c.

  10. ANSWER = – (m – 1)(5m – 1) 8. – 5m2 + 6m – 1 STEP 1 Factor – 1 from each term of the trinomial. – 5m2 + 6m – 1 = – (5m2 – 6m + 1) STEP 2 Factor the trinomial 5m2 – 6m + 1. Because bis negative and cis positive, the factors of cmust be both negative. Use a table to organize information about the factors of aand c.

  11. ANSWER – 3x2 – x + 2 = – (x + 1)(3x – 2) 9. – 3x2 – x + 2 STEP 1 Factor – 1 from each term of the trinomial. – 3x2 – x + 2 = – (3x2 + x – 2) STEP 2 Factor the trinomial 3x2 + x – 2. Because bis positive and cis negative, the factors of cmust have different signs. Use a table to organize information about the factors of aand c.

  12. HOMEWORK Worksheet

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