Factoring Trinomials Puzzle



Alg 2: Unit 2

“Always check for GCF of original polynomial first”

FACTORING NO Leading Coefficient Trinomials x2 + bx + c = (x + ?) (x + ?)

Step #1: Find the factor pair (n1 and n2) that MULTIPLY = c (outside) and ADD = b (middle).

Step #2: Split the middle term bx = n1x + n2x

Step #3: Perform factor by grouping on x2 + n1x + n2x + c = (x + ?) (x + ?)

Exp 1: Factor x2 + 6x + 8

Step #1: 2 • 4 = 8, 2 + 4 = 6

Step #2: x2 + 2x + 4x + 8

Step #3: x(x+2) + 4(x + 2)

(x + 2) (x + 4)

Exp 2: Factor 3b2 – 30b + 48

Original GCF = 3; b2 – 10b + 16

Step #1: -2 • -8 = 16; -2 + -8 = -10

Step #2: b2 – 2b – 8b + 16

Step #3: b(b – 2) -8 (b – 2)

3(b - 2) (b - 8)

Exp 3: Factor x2 + 2xy – 15y2

Step #1: -3• 5 = -15; -3 + 5 = 2

Step #2: x2 + 5xy – 3xy – 15y2

Step #3: x(x + 5y) – 3y(x +5y)

(x + 5y) (x – 3y)

Factor each completely: Use separate piece of paper as needed

1. x2 + 6x + 5

2. 4a2 + 28a + 40

3. x2 – 7x + 12

4. x2 – 11x + 28

5. 2x2 – 10x – 30

6. y2 – 5y – 24

7. x2 + x – 56

8. x2 + 10x + 16

9. a2 – 15a + 50

10. n2 + 8n – 9

11. x2 – 7x – 30

12. x2 – x – 30

13. x2 – 4xy + 3y2

14. r2 + 13rs – 48s2

15. a2 – 17ab + 60b2

Alg 2: Unit 2

“Always check for GCF of original polynomial first”

FACTORING Leading Coefficient Trinomials ax2 + bx + c = (?x + ?) (?x + ?)

Step #1: Find the factor pair (n1 and n2) that MULTIPLY = ac (outside) and ADD = b (middle).

Step #2: Split the middle term bx = n1x + n2x

Step #3: Perform factor by grouping on ax2 + n1x + n2x + c = (?x + ?) (?x + ?)

Exp 1: 6x2 + 17x + 5

a•c = 6•5 = 30

Step #1: 2•15 = 30; 2 + 15 = 17

Step #2: 6x2 + 2x + 15x + 5

Step #3: 2x(3x + 1) + 5(3x + 1)

(2x + 5) (3x + 1)

Exp 2: 5z2 – 7z – 6

a•c = 5•-6 = -30

Step #1: 3•-10 = -30; 3 + -10 = -7

Step #2: 5z2 + 3z –10z – 6

Step #3: z(5z + 3) – 2(5z + 3)

(z – 2) (5z + 3)

Exp 3: 12y2 – 34y + 14

Overall GCF = 2: 6y2 – 17y + 7

a•c = 6•7 = 42

Step #1: -3•-14 = 42; -3 + -14 = -17

Step #2: 6y2 – 3y – 14y + 7

Step #3: 3y(2y – 1) – 7(2y – 1)

2(3y – 7) (2y – 1)

Factor each completely: Use separate piece of paper as needed

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