Lesson 8-5 Warm-Up

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Lesson 8-5 Warm-Up
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Factoring Trinomials of the Type x2 bx c
(8-5)

• What is a trinomial?
• How do you factor a trinomial?

• Trinomial a polynomial that consists of three
  unlike terms
• Examples x2 7x 12 x2 bx c
• To factor a trinomial of the form x2 bx c,
  you must find two numbers that have a sum of b
  and a product of c
• Example Factor x2 7x 12
• Notice that the coefficient of the middle term, b
  or 7, is the sum of 3 and 4. Also, the constant,
  c or 12, is the product of 3 and 4. Therefore,
  you can now create two binomials whose product is
  x 2 7x 12.
• x 2 7x 12. (x 3)(x 4)
• Check Does (x 3)(x 4) x 2 7x 12?
• (x 3)(x 4) x 2 4x 3x 12 FOIL
• x 2 7x 12 ? Combine like terms.

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Factoring Trinomials of the Type x2 bx c
(8-5)

• How do you find two numbers that have a sum of b
  and a product of c?

• Method 1 Create a Table Title one column
  Factors of (Constant) or Factors of c and
  the other column Sum of the Factors. Then, fill
  in the table with the number pairs that are
  factors of the constant.
• Example Factor x2 7x 12
• To factor this polynomial, well need to find
  factors pairs of 12 (two numbers whose product is
  12) whose sum is 7. To do this create a table.

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Factoring Trinomials of the Type x2 bx c
(8-5)

• Method 2 Use an Area Model in Reverse Arrange
  the Algebra Tiles that model the trinomial into a
  rectangle. The sides of the rectangle (length and
  width) are the factors of the trinomial. Tip
  Think about how to end with the number of desired
  1 tiles.
• Example Factor x2 7x 12

n
n
n
n
x 4
x2
x
x
x
x
3n 1
3n 1
x 3
x 3
x
1
1
1
1
x
1
1
1
1
x
1
1
1
1
x 4
n
n
2n 7
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Factoring Trinomials of the Type x2 bx c
(8-5)

• Example Factor d2 17d 42
• To factor this polynomial, well need to find
  factors pairs of 42 (two numbers whose product is
  42) whose sum is -17. To do this create a table.
• So, d2 - 17x 42 (d - 3)(d - 14)
• Check Does (d -3)(d - 14) d 2 - 17x 42?
• (d -3)(d - 14) d 2 3d 14d 42 FOIL
  
• d2 17d 12 ? Combine like
  terms.

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Factoring Trinomials of the Type x2 bx c
LESSON 8-5
Additional Examples
Factor x2 8x 15.
Find the factors of 15. Identify the pair that
has a sum of 8.
x2 8x 15 (x 3)(x 5).
x2 5x 3x 15
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Factoring Trinomials of the Type x2 bx c
LESSON 8-5
Additional Examples
Factor c2 9c 20.
Since the middle term is negative, find negative
factors of 20 (a negative times a negative equals
a positive).
Identify the pair that has a sum of 9.
c2 9c 20 (c 5)(c 4)
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Factoring Trinomials of the Type x2 bx c
LESSON 8-5
Additional Examples
a. Factor x2 13x 48.
b. Factor n2 5n 24.
Identify the pair of factors of 48 that has a
sum of 13.
Identify the pair of factors of 24 that has a
sum of 5.
x2 13x 48 (x 16)(x 3)
n2 5n 24 (n 3)(n 8)
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Factoring Trinomials of the Type x2 bx c
LESSON 8-5
Additional Examples
Factor d 17dg 60g .
2
2
d2 17dg 60g2 (d 3g)(d 20g)
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Factoring Trinomials of the Type x2 bx c
LESSON 8-5
Lesson Quiz
Factor each expression. 1. c2 6c 9 2. x2
11x 18 3. g2 2g 24 4. y2 y 110 5. m2
2mn n2
(c 3)(c 3)
(x 2)(x 9)
(g 6)(g 4)
(y 11)(y 10)
(m n)(m n)