Solving Quadratic Equations by Factoring Zero Factor Property ...

Solving Quadratic Equations by Factoring Objective: To use the zero factor property to solve equations.

Steps for Solving Quadratic Equations w/ Factoring

Zero Factor Property {

If ab = 0, then a = 0 or b = 0 or both a and b = 0.

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2. {

In other words, if a product is zero, then one or all of the factors are zero.

3. 4. 5.

Examples – SOLUTIONS

Examples – Solve each equation. {

a) (2x+3)(x-5)=0

b)

x2 –36 = 0

Put equation in standard form. (ax2 + bx + c = 0) Factor completely. Set each factor = 0. Solve each equation. Check. (VERY IMPORTANT!)

{

a) (2x+3)(x-5)=0

{

(already factored and set = 0, so…)

{

b)

x2 –36 = 0

2 x + 3 = 0 or x − 5 = 0 ( x + 6)( x − 6) = 0 x + 6 = 0 or x − 6 = 0 2 x = -3 or x = 5

−3 2 ⎧ −3 ⎫ x = ⎨ , −5⎬ ⎩2 ⎭ x=

x = −6

x=6

x = {−6, 6}

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Examples {

c)

a2

Examples -- SOLUTIONS

–24a =-144

d)

-3m2

+ 27m = 0

{

c)

a2

–24a =-144

d) -3m2 + 27m = 0

a 2 − 24a + 144 = 0

−3m 2 + 27 m = 0

(a − 12)(a − 12) = 0

−3m(m − 9)) = 0

a = 12

−3m = 0 or m − 9 = 0

a = {12}

m=0

or

m=9

m = {0,9}

More Examples e) m2 - 25=24m

f) x3 + 2x2= 15x

SOLUTIONS e) m2 – 25= 24m

f) x3 + 2x2= 15x

m − 24m − 25 = 0 (m − 25)(m + 1) = 0 m − 25 = 0 or m + 1 = 0

x3 + 2 x 2 − 15 x = 0

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m = {25, −1}

Here’s a real doozy… { g)

(3x+2)(x–3) = 7x - 1

x( x 2 + 2 x − 15) = 0 x( x + 5)( x − 3) = 0 x = 0 or x + 5 = 0 or x − 3 = 0 x = {0, −5,3}

SOLUTION { g) (3x+2)(x–3) = 7x - 1 (3 x + 2)( x − 3) = 7 x − 1 3x2 − 9x + 2x − 6 − 7 x + 1 = 0 3 x 2 − 14 x − 5 = 0 (3 x + 1)( x − 5) = 0 3 x + 1 = 0 or x − 5 = 0 3 x = − 1 or x=5 -1 3 ⎧ −1 ⎫ x = ⎨ , 5⎬ ⎩ 3 ⎭

x=

2

SUMMARY { { { {

Put equation in standard form. Factor. Set each factor = 0 and solve. Check.

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