1. Warm-Up 2.3 Factor each. 36 – x2 15x4y2 – 20x2y3 + 5x3y4

2. Lesson 2.3 Algebra 3 Objective: SSBAT factor trinomials.
Teacher
Algebra 3
Lesson 2.3
Objective: SSBAT factor trinomials.
Standards: M11.D.2.2.2

3. Analyze each. (x + 7)(x + 4) = x2 + 11x + 28
Sum of 7 and 4
Product of 7 and 4
(x + 6)(x – 4) = x2 + 2x – 24
Sum of of 6 and -4
Product of 6 and -4

4. Recall:
Factoring  Rewriting an expression as a Multiplication Problem

5. Factoring Trinomials of the Form x2 ± bx ± c
List the pair of factors for c
 If c is positive – the factors will have the same sign
 If c is negative – 1 factor will be positive and will be negative
2. Find the pair from above that have a sum of b
3. Write in the form (x ± #)(x ± #)
The 2nd number of each will be the factors from step 2

6. Factored Form: (x + 5)(x + 8)
Teacher
Examples: Factor each trinomial.
1. x2 + 13x + 40
Factors of +40
The SUM of each
1, 40
2, 20
4, 10
5, 8 41 22 14 13
* You need the pair with a sum of 13, since that is what is in front of the x term. *
Therefore use the factors 5 and 8
Factored Form: (x + 5)(x + 8)

7. (x + 5)(x + 8) = x2 + 8x + 5x + 40 = x2 + 13x + 40 Its Checks.
Check  FOIL through and see if you get back to the beginning expression.
(x + 5)(x + 8)
= x2 + 8x + 5x + 40
= x2 + 13x + 40
Its Checks.

8. (x – 1)(x – 8) 2. x2 – 9x + 8  Note: the x term is negative: -9x
Teacher
x2 – 9x + 8
 Note: the x term is negative: -9x
 Need the negative factors of positive 8
Negative Factors of 8
Sum of each (-9)
-1, -8
-2, -4 -9 -6
(x – 1)(x – 8)

9. Check  FOIL through and see if you get back to
Check  FOIL through and see if you get back to the beginning expression.
(x – 1)(x – 8)
= x2 – 8x – 1x + 8
= x2 – 9x + 8
Checks.

10. 3. y2 – 17y + 42 (y – 3)(y – 14) Negative factors of 42
Teacher
y2 – 17y + 42
Negative factors of 42
Sum of each (-17)
-1, -42
-2, -21
-3, -14
-6, -7
-43
-23
-17
-13
(y – 3)(y – 14)

11. Factored Form: (x – 4)(x + 5)
Factors of -20
Sum of each (1)
1, -20
-1, 20
2, -10
-2, 10
4, -5
-4, 5
-19 19 -8 8 -1 1
Factored Form: (x – 4)(x + 5)

12. Factored Form: (x + 2)(x – 7)
Factors of -14
Sum of –5
1, -14
-13
-1, 14 13
2, -7 -5
Factored Form: (x + 2)(x – 7)

13. x2 + 8x + 20
Prime – Cannot Factor

14. On Your Own.
1. x2 + 14x – 72
2. x2 + 17x + 60

15. Homework
Worksheet 2.3
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