Solving Equations by Factoring

Standard Form Quadratic Equation

Quadratic equations can be written in the form

ax2 + bx + c = 0where a, b, and c are real numbers with a 0.

Standard form for a quadratic equation is in descending order equal to zero.

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Examples of Quadratic Equations

pp 18812

1892 xx

252 y

081182 pp

Standard Form

01892 xx

0252 y

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Zero Product 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.

0)2( x2x

OR (2 1) 0x 12 x

2

1

2

2

x 2

1x

}2

1,2{x

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Solve the equation. Check your answers.

0)2)(5( xx

5xOR 02 x

2x { 2, 5}x 05 x Solution Set

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Solve each equation. Check your answers.

0)35( xx

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Solving a Quadratic Equation by Factoring

Step 1: Standard form, =0Step 2: FactorStep 3: Use ZPP to set each factor =0Step 4: Solve each equation

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Solve.

x 2 12x 36 0

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Solve.

822 rr

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Solve.

6m2 13m 6 0

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4x2 – 49 = 0

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Solve.

072 xx

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Solve.

1892 xx

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