Quadratic equations

3.4 Solving Quadratic Equations by Factoring

Get out a piece of paper and a pencil

There are several ways to solving a quadratic equation.

• 1) Graphing: Put the equation in Desmos and find the x-intercepts (zeros).

• 2) Factoring: Factor the trinomials, set each factor equal to zero, then solve for the indicated variable.

• 3) Quadratic Formula

• 4) Complete the Square

Multiple Choice

What are the solutions?

• 0 and 8

• -2 and -4

• 3 and -1

• 2 and 4

Now: Zero Product Property

• For any real number a and b, if ab=0 then a=0, b=0, or both a nd b are zero.

• Basically the only way to multiply and get zero is to multiply by zero.

Multiple Choice

Solve using Zero-Product Property.

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

• x = -1

• x = -1 or x = 1

• x = 1

• x = -2 or x = 5

Multiple Choice

Solve by factoring:
x² - 9x = 0

• 9

• 0, 9

• -9, 0

• -9

Multiple Choice

Solve the equation using the zero product property.

3x(2x - 4) = 0

• x = -1/3 or x = -2

• x = 0 or x = 2

• x = 0 or x = -2

• x = -1/3 or x = 2

Multiple Choice

Solve by factoring

• -4, 2

• -2, 4

• -16

• -4

Multiple Choice

$$x^2=11x-28$$  

• $$7,\ 4$$

• $$-5,\ 0$$  
  

• $$2,\ 0$$  

Multiple Choice

$$3m^2=-16m-21$$  

• $$7,\ 4$$

• $$-\frac{5}{8},\ 6$$  
  

• $$-\frac{7}{3},\ -3$$  

Multiple Choice

$$x^2+17x+49=3x$$

• $$-7$$

• $$-8,\ -7$$
  

• $$3,\ 6$$

Multiple Choice

$$7p^2-38p-24=0$$

• $$-\frac{7}{2},\ 2$$

• $$-\frac{4}{7},\ 6$$
  

• $$\frac{3}{5},\ 2$$

Multiple Choice

Solve.  3x² - 27x = 0 

• x = 3,    x = -3
• x = 0,    x = 9
• x = -27
• x = 0,    x = 3

Multiple Choice

Solve
16a² - 9 = 0

• a = ^-3/₄, ³/₄ 
• a = ^-4/₃, ⁴/₃ 
• a = ^-9/₁₆, ⁹/₁₆ 
• a = ^-16/₉, ¹⁶/₉ 

Multiple Choice

The length of a rectangle is 4 cm more than its width. The area of the rectangle is 96 sq. cm. Find its dimensions.

• 4 cm by 8 cm

• 6 cm by 10 cm

• 8 cm by 12 cm

• 10 cm by 14 cm