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Factoring Trinomials of the form x 2 + bx + c Chapter 5.3

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Review Multiplying Two Binomials (FOIL)

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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 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.

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x2x2 1. GCF = (x ) + 2 (x ) + 6 + 8+ 12 2. Factor first term. 1. Factor. 1 3. Find 2 integers whose product is 12 and sum is 8. 1, 12 2, 6 x

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x2x2 1. GCF = (x ) + 2 (x ) + 15 + 17+ 30 2. Factor first term. 2. Factor. 1 3. Find 2 integers whose product is 30 and sum is 17. 1, 30 2, 15 x

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x2x2 1. GCF = (x ) – 2 (x ) – 9 – 11+ 18 2. Factor first term. 3. Factor. 1 3. Find 2 integers whose product is 18 and sum is -11. -1, -18 -2, -9 x

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x2x2 1. GCF = (x ) – 3 (x ) – 8 – 11+ 24 2. Factor first term. 4. Factor. 1 3. Find 2 integers whose product is 24 and sum is -11. -1, -24 -2, -12 -3, -8 x

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x2x2 1. GCF = (x ) + 3 (x ) – 8 – 5– 24 2. Factor first term. 5. Factor. 1 3. Find 2 integers whose product is -24 and sum is -5. 1, -24 2, -12 3, -8 x

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y2y2 1. GCF = (y ) – 3 (y ) + 20 + 17– 60 2. Factor first term. 6. Factor. 1 3. Find 2 integers whose product is -60 and sum is 17. -1, 60 -2, 30 -3, 20 y

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x2x2 1. GCF = (x ) + 5 (x ) – 12 – 7– 60 2. Factor first term. 7. Factor. 1 3. Find 2 integers whose product is -60 and sum is -7. 1, -60 2, -30 3, -20 4, -15 5, -12 x

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a4a4 1. GCF = (a 2 ) – 6 (a 2 ) + 7 +– 42 2. Factor first term. 8. Factor. 1 3. Find 2 integers whose product is -42 and sum is 1. -1, 42 -2, 21 -3, 14 -6, 7 a2a2 1

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3( ) x 2 1. GCF = (x ) + 5 (x ) + 10 + 15+ 50 2. Factor first term. 9. Factor. 3 3. Find 2 integers whose product is 50 and sum is 15. 1, 50 2, 25 5, 10 x 3+ 45+ 150 x x2x2 3

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4( ) x 2 1. GCF = (x ) + 5 (x ) – 7 – 2– 35 2. Factor first term. 10. Factor. 4 3. Find 2 integers whose product is -35 and sum is -2. 1, -35 5, -7 x 4– 8– 140 x x2x2 4

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

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Factoring Trinomials of the form x 2 + bx + c Chapter 5.3

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