Section 5'6 Solving Equations by Factoring

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Section 5.6Solving Equations by Factoring

• Definition of Quadratic Equations
• Zero-Factor Property
• Strategy for Solving Quadratics

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Definition of Quadratic Equation

• Quadratic equations can be written in the form
• ax2 bx c 0
• where a, b, and c are real numbers with a ? 0.

Most equations with the highest exponent 2 are
quadratic equations.
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Examples of Quadratic Equations
Standard Form
Setting quadratics equal to 0 is very important
for the next thing.
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Zero-Factor Property

• If a and b are real numbers
• and if ab 0, then
• a 0 or
• b 0.

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Solve the equation (x 2)(2x - 1)0

• By the zero factor property we know...
• Since the product is equal to zero then one of
  the factors must be zero.

OR
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Solve the equation. Check your answers.
Solution Set
OR
Check x 5
Check x -2
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Solve each equation. Check your answers.
OR
Solution Set
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Solve each equation. Check your answers.
Solution Set
TRUE
TRUE
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Solve each equation. Check your answers.
OR
Solution Set
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Solve.
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Solving a Quadratic Equation by Factoring Page 322

• Step 1 Write the equation in standard form.
• Step 2 Factor completely.
• Step 3 Use the zero-factor property. Set each
  factor with a variable equal to zero.
• Step 4 Solve each equation produced in step 3.
• Step 5 Check each solution in the original
  equation.

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Solve.
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Check m 5, -2 m2-3m-100
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Solve.
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Solve.
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Check r -4, 2 r2 2r 8
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Solve.
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Solve.
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Homework

• Problem Set 5.6
• Page 333
• 1-85 odd

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HW 5.6 5 Solve.

• x (x 1)(x 3) 0
• Set each of the three factors equal to 0.

x 0
x 1 0
x 3 0
x -1
x 3
Solve the resulting equations.
x 0, -1, 3
Write the solution set.
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HW 5.6 15 Solve.

• x2 9x 20 0
• (x 4)(x 5) 0
• x 4 0
• x 4
• x 5 0
• x 5
• x 5, 4

• Standard form already
• Factor
• Set each factor 0
• Solve
• Write the solution set

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HW 5.6 25 Solve.

• 2x2 5x 12 0
• (2x 3)(x 4) 0
• x 4 0
• x -4
• 2x 3 0

• Standard form already
• Factor
• Set each factor 0
• Solve
• Write the solution set

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HW 5.6 35 Solve.

• 4x2 49 0
• (2x 7)(2x 7) 0
• 2x 7 0
• 2x 7 0

• Standard form already
• Factor
• Set each factor 0
• Solve
• Write the solution set

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HW 5.6 45 Solve.

• 1400 400 700x 100x2
• 100x2 - 700x 1000 0
• 100(x2 - 7x 10) 0
• 100(x 5)(x 2) 0
• x 5 0
• x 5
• x 2 0
• x 2
• x 5, 2

• Write in standard form
• GCF 100
• Factor
• Set each factor 0
• Solve
• Write the solution set

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Which would you like to see?

• 43. 3x2 15x
• 47. 6x2 -5x 4
• 49. x(2x 3) 20
• 53. 4000 (1300 100p)p
• 61. 102 (x 2)2 x2