Zero Product Property Polynomials

Solving Polynomial Functions:
The Zero Product Property

Multiple Choice

Factor:

x² + 11x + 24

• (x + 6)(x + 4)

• (x + 12)(x + 2)

• (x - 8)(x - 3)

• (x + 8)(x + 3)

Multiple Choice

What are the factors of 3x²-17x+10

• (x-5)(3x-2)
• (x+5)(3x+2)
• (3x-5)(x-2)
• (x+5)(3x-2)

Multiple Choice

Find the factors of 5x²+20x+20

• 5(x+2)(x+2)
• 5(x-2)(x-2)
• 5(x+2)(x-2)
• (5x+2)(x+2)

Zero Product Property

Steps:
1. Make sure polynomial is in standard form=0
2. Factor the polynomial completely.
3. Set each factor=0 and solve.
4. Write your answers as a solution set.
Here is a video

Multiple Choice

Solve for the values of x:
(x - 3)(x + 6) = 0

• { -3, -6 }
• { 3, -6 }
• { -3, -6 }
• { 3, 6 }

Multiple Choice

Factor Completely: 
3x² + 18x +15
Hint: Factor GCF first.

• 3(x² + 6x + 5)
• (x + 5)(x + 1)
• 3(x + 5)(x + 1)
• Prime

Multiple Choice

Solve:

3x² + 18x +15 = 0

Hint: Factor GCF first.

• x = 3, 2

• x = 5, 1

• x = -5, -1

• x = -3, -2

Multiple Choice

Factor Completely:

x² - 49

• (x - 7)(x - 7)
• (x - 49)(x + 1)
• (x - 14)(x + 14)
• (x - 7)(x + 7)

Multiple Choice

Solve:

x² - 49 = 0

• x = -7, x = 7

• x = -7

• x = 7

• x = -7, x = 1

Multiple Choice

Solve: $$\left(5x+4\right)\left(x-2\right)=0$$

• x = -4/5, x = 2
• x = 2, x = -4

• x = -2, x = 4
• x = 0, x = 2

Multiple Choice

Solve:  $$2x^2-15=x$$  

Remember to rearrange the equation into standard form=0.

• $$x=-\frac{5}{2}$$  and  $$x=3$$  

• $$x=\frac{5}{2}$$  and  $$x=-3$$  

• $$x=\frac{5}{2}$$  and  $$x=3$$  

• $$x=-\frac{5}{2}$$  and  $$x=-3$$  

Multiple Choice

Solve:

k² - 2k = 24

• k = -4, 6

• k = -4, -6

• k = -6, 1

• k = 4, -6

Multiple Choice

Solve: $$x^2-5x+6=0$$

• x = 2, x = 3
• x = 0, x = 5
• x = -2, x = -3
• x = 1, x = 4

Multiple Choice

Solve: $$-4k^2-8k-3=-3-5k^2$$

• k = 2
• k = 4
• k = 0 or k = 8
• k = -1

Multiple Choice

Solve: $$3b^3-4b^2-27b=-36$$

• b = 3, 4/3

• b = -3, -9

• b = 3, 9

• b = 3, -3, 4/3