7'2 Factoring Trinomials Whose Leading Coefficient is 1

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7.2 Factoring Trinomials Whose Leading
Coefficient is 1

• Objective
• Factoring trinomials of the form x2 bx c

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7.2 Objective 1 Factoring Trinomials of the
form 1x2 bx c

• 1. Enter x as the first term of each factor
• x2 bx c ( x ) ( x )
• 2. To determine the second term of each factor
• a) Find all pairs of integers whose product is
  c, the third term of the trinomial.
• b) Choose the pair whose sum is b, the
  coefficient of the middle term of the trinomial.

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7.2 Objective 1 Factoring Trinomials of the
form 1x2 bx c

• b) Choose the pair whose sum is b, the
  coefficient of the middle term of the trinomial.
• c) If mn c and m n b, then m and n are the
  desired integers, and
• x2 bx c ( x m ) ( x n )
• 3. If there are no such integers, the trinomial
  cannot be factored and is called prime.

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7.2 Application problem

• Consider a person standing at the edge of a cliff
  who throws a rock upward with an initial speed of
  64 feet per second. His hand at the time of
  release is 80 feet above the water. After t
  seconds, the height h of the rock above the water
  is described by the model
• h -16t 2 64t 80
• Factor this polynomial completely. Begin by
  factoring 16 from each term.

80 ft
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7.2 Application problem continued

• h -16t 2 64t 80
• Factor this polynomial completely. Begin by
  factoring 16 from each term.
• How can we determine how long it takes for the
  rock to enter the water?

80 ft
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7.2 Objective 1 Factoring Trinomials of the
form 1x2 bx c Revisited

• Find two integers m and n whose product is c and
  whose sum is b. If mn c and m n b, then
• x2 bx c ( x m ) ( x n )
• 1. If b gt 0 and c gt 0, m and n must be positive.
• 2. If b lt 0 and c gt 0, m and n must be negative.
• 3. If c lt 0, m and n must have opposite signs.

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7.2 Objective 1 Factoring Trinomials of the
form 1x2 bx c Revisited

• Try p 412 46, 53 Remember to first remove any
  GCF!
• 1. If c gt 0 m and n must be the same sign!!
• If b gt 0 and c gt 0, m and n must be positive.
• If b lt 0 and c gt 0, m and n must be negative.
• 2. If c lt 0, m and n must have opposite signs.

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7.2 Objective 1 Factoring Trinomials of the
form 1x2 bx c Revisited

• Try p 412 46, 53 Remember to first remove any
  GCF!
• 1. If c gt 0 m and n must be the same sign!!
• If b gt 0 and c gt 0, m and n must be positive.
• If b lt 0 and c gt 0, m and n must be negative.
• 2. If c lt 0, m and n must have opposite signs.

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7.2 Objective 1 Factoring Trinomials of the
form 1x2 bx c

• P410
• Example 5 A prime polynomial that wont factor.
• Example 6 Factoring a Trinomial in Two Variables
• Example 7 Factoring Completely.