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Factoring Trinomials of the form x 2 + bx + c

Chapter 5.3. Factoring Trinomials of the form x 2 + bx + c. Review Multiplying Two Binomials (FOIL). Factoring x 2 + bx + c. 1. Check each term to see if there is a GCF of all terms. 2. Factor the first term in the trinomial and write it as the 1 st

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Factoring Trinomials of the form x 2 + bx + c

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  1. Chapter 5.3 Factoring Trinomials of the form x2 + bx + c

  2. Review Multiplying Two Binomials (FOIL)

  3. Factoring x2 + bx + c 1. Check each term to see if there is a GCF of all terms. 2. Factor the first term in the trinomial and write it as the 1st term in both binomials (x )(x ) 3. Find two numbers (m and n) such that the product is c and the sum is b. 4. Write: (x + m)(x + n). 5. Depending on the sign of b and c the numbers you are finding (m and n) could be positive or negative.

  4. 0 1. Factor. 1. GCF = 1 x x2 + 8 + 12 2. Factor first term. 3. Find 2 integers whose product is 12 and sum is 8. (x ) (x ) + 2 + 6 1, 12 2, 6

  5. 0 2. Factor. 1. GCF = 1 x x2 + 17 + 30 2. Factor first term. 3. Find 2 integers whose product is 30 and sum is 17. (x ) (x ) + 2 + 15 1, 30 2, 15

  6. 0 3. Factor. 1. GCF = 1 x x2 – 11 + 18 2. Factor first term. 3. Find 2 integers whose product is 18 and sum is -11. (x ) (x ) – 2 – 9 -1, -18 -2, -9

  7. 0 4. Factor. 1. GCF = 1 x x2 – 11 + 24 2. Factor first term. 3. Find 2 integers whose product is 24 and sum is -11. (x ) (x ) – 8 – 3 -1, -24 -2, -12 -3, -8

  8. 0 5. Factor. 1. GCF = 1 x x2 – 5 – 24 2. Factor first term. 3. Find 2 integers whose product is -24 and sum is -5. (x ) (x ) – 8 +3 1, -24 2, -12 3, -8

  9. 0 6. Factor. 1. GCF = 1 y y2 + 17 – 60 2. Factor first term. 3. Find 2 integers whose product is -60 and sum is 17. (y ) (y ) + 20 – 3 -1, 60 -2, 30 -3, 20

  10. 0 7. Factor. 1. GCF = 1 x x2 – 7 – 60 2. Factor first term. 3. Find 2 integers whose product is -60 and sum is -7. (x ) (x ) – 12 + 5 1, -60 2, -30 3, -20 4, -15 5, -12

  11. 0 8. Factor. 1. GCF = 1 a2 a4 + – 42 1 2. Factor first term. 3. Find 2 integers whose product is -42 and sum is 1. (a2 ) (a2 ) + 7 – 6 -1, 42 -2, 21 -3, 14 -6, 7

  12. 0 9. Factor. 1. GCF = 3 x 3 + 45 + 150 x2 2. Factor first term. 3( ) x x2 + 15 + 50 3. Find 2 integers whose product is 50 and sum is 15. (x ) (x ) 3 + 5 + 10 1, 50 2, 25 5, 10

  13. 0 10. Factor. 1. GCF = 4 x 4 – 8 – 140 x2 2. Factor first term. 4( ) x x2 – 2 – 35 3. Find 2 integers whose product is -35 and sum is -2. (x ) (x ) 4 + 5 – 7 1, -35 5, -7

  14. 0 11. Find a polynomial in factored form for the shaded (green) area in the figure. A = x(x + 1) – (4)(5) Multiply x x2 + – 20 1 1. GCF = 1 2. Factor first term. (x ) (x ) + 5 – 4 3. Find 2 integers whose product is -20 and sum is 1. -1, 20 -2, 10 -4, 5 4 x 5 x + 1

  15. Chapter 5.3 Factoring Trinomials of the form x2 + bx + c

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