Factored Form: (x + 2)(x + 6) Does this product result in our original expression x2 + 6x + 8? Double distribute to find out! (x + 2)(x + 4) x2 + 4x + 2x + 8

x2 + 6x + 8

Pre-Algebra

Essential Question: How do we factor trinomials in the form of x2 + bx + c?

Lesson Summary

Factoring a trinomial in the form of x2 + bx + c

Step 1: Identify the b and c (numerical) values in the trinomial.

Step 2: Identify all pairs of factors that multiply to the c value (last term).

Step 3: Determine which pair adds to the b value (coefficient of middle term). Step 4: Create 2 sets of parentheses whose first term is x.

Step 5: Place the factors in the parentheses to create two binomials.

Step 6: Check by multiplying the factors (double distribute).

Factor x2 + 6x + 8 using the steps above

1) x2 + 6x + 8 b = 6 and c = 8

2) Factors of 8 are as follows: 1 x 8 and 2 x 4 and -1 x -8 and -2 x -4

3) The factor pair that adds to 6 is 2 and 4 because 2 + 4 = 6

4) (x )(x )

5) (x + 2)(x + 4) or (x + 4)(x + 2)

6) Check your work!

Before reviewing the lesson and completing the practice problem set, watch the VIDEO!

The factored form of x

2 + 6x + 8

is (x + 2)(x + 4)

(x + 1)(x – 12) x2 – 12x + 1x – 12

x2 – 11x – 12

Examples

Factor each trinomial using the AM method. Note: We call this method of factoring AM because we ask the question:

"What numbers MULTIPLY to the last term (c) and ADD to the coefficient of the middle term (b)?"

1. x2 + 7x + 12

(x )(x ) 2. x2 – 7x + 12

(x )(x ) 3. x2 + 11x – 12

(x )(x )

4. x2 – 11x – 12

(x )(x )

Reminder: Always check to make sure that the factored form is equivalent to the original polynomial expression! Check for #4:

x2 + 7x + 12 What numbers multiply to 12? 1, 12 -1, -12 Which pair adds to 7? 2, 6 -2, -6 3, 4 -3, -4 The factored form of x2 + 7x + 12 is (x + 3)(x + 4)

x2 – 7x + 12 What numbers multiply to 12? 1, 12 -1, -12 Which pair adds to -7? 2, 6 -2, -6 3, 4 -3, -4 The factored form of x2 – 7x + 12 is (x – 3)(x – 4)

x2 + 11x – 12 What numbers multiply to -12? -1, 12 1, -12 Which pair adds to 11? -2, 6 2, -6 -3, 4 3, -4 The factored form of x2 + 11x – 12 is (x – 1)(x + 12)

x2 – 11x – 12 What numbers multiply to -12? -1, 12 1, -12 Which pair adds to -11? -2, 6 2, -6 -3, 4 3, -4 The factored form of x2 – 11x – 12 is (x + 1)(x – 12)

**Patterns to Notice:

1. If b and c are both positive, both of the binomials have + signs. Ex: x2 + 6x + 8 = (x + 2)(x + 4)

2. If c is negative, one binomial has a + sign and one has a - sign. Ex: x2 + 11x – 12 = (x – 1)(x + 12)

3. If c is positive and b is negative, both binomials have a - sign. Ex: x2 – 7x + 12 = (x – 3)( x – 4)

Practice Problem Set

ATTENTION ALL PRE-ALGEBRA STUENTS: We want to remind you that you and your peers create a learning community. We encourage you to face time, text or use any other appropriate communication to reach out to a friend and discuss your answers to the following questions. Working together and having meaningful mathematical discussions aids in your understanding of the subject matter.

Factor each trinomial using the AM method. 1. x2 + 8x + 15 2. x2 + 9x + 18 3. x2 + 14x + 24 4. x2 – 10x + 9 5. x2 – 8x – 20 6. x2 + x – 12