Zero Product Property

Show your work for each problem.

1.
What does the Zero Product Property state?
1. a)If , then or
2. b)If , then
3. c)If , then or
4. d)If , then and
Answer: If , then or
The Zero Product Property states: if , then or (or both). This is because zero is the only number that, when multiplied with anything, gives zero.
2.
Solve: . What is the positive solution?
Answer: 4
Setting each factor to zero: gives , and gives . The positive solution is .
3.
Solve: . What is the larger solution?
Answer: 6
The factors are and . Setting each to zero: or . The larger solution is .
4.
Why can't we apply the Zero Product Property to ?
1. a)The product is not equal to zero
2. b)The equation is quadratic
3. c)There are only two factors
4. d)The factors are too simple
Answer: The product is not equal to zero
The Zero Product Property ONLY works when the product equals zero. When , we can't conclude anything about or individually (could be , , etc.).
5.
Solve
Answer: -5, 2
1. Using Zero Product Property, what is the first equation? x + 5 = 0
2. Solve . What is ? -5
3. What is the second equation? x - 2 = 0
4. Solve . What is ? 2
6.
Solve . What is the negative solution?
Answer: -4
means or . From , we get . From , we get . The negative solution is .
7.
How many solutions does have?
1. a)2
2. b)1
3. c)0
4. d)3
Answer: 0
There are 3 factors: , , and . Setting each to zero: , , . Three solutions.
8.
Solve by factoring first
Answer: 4, 5
1. Find two numbers that multiply to 20 and add to -9 -4 and -5
2. Write the factored form (x - 4)(x - 5) = 0
3. What is the first solution? 4
4. What is the second solution? 5
9.
Solve . What is the sum of both solutions?
Answer: -2
. Solutions: or . Sum: .
10.
Solve
Answer: 0, 4
1. What is the GCF of and ? 2x
2. Factor out the GCF. What is the factored form? 2x(x - 4) = 0
3. Set the first factor equal to zero. What is ? 0
4. Set the second factor equal to zero. What is ? 4
11.
What mistake was made? Student work: , divide by , so , thus .
1. a)Lost the solution by dividing
2. b)The equation was already solved
3. c)Should have added 5 instead
4. d)Factoring was done incorrectly
Answer: Lost the solution by dividing
By dividing by , the student lost as a solution. Verify: \checkmark. The complete answer is or .
12.
Solve using the difference of squares
Answer: -4, 4
1. Rewrite as . What is ? x
2. What is ? 4
3. Factor using (x - 4)(x + 4) = 0
4. List both solutions 4 and -4
13.
Solve . What is the product of both solutions?
Answer: 0
. Solutions: or . Product: .
14.
How many solutions does have?
1. a)0
2. b)2
3. c)1 (double root)
4. d)Infinitely many
Answer: 0
has only one distinct solution: . This is called a double root because the factor appears twice.
15.
A ball's height is meters. When does it hit the ground?
Answer: 3
1. Set height equal to zero -5t^2 + 15t = 0
2. Factor out the GCF -5t(t - 3) = 0
3. List both solutions for 0 and 3
4. Which solution represents landing time (not launch)? 3
16.
Solve
Answer: -1/2, 5
1. Set the first factor equal to zero 2x + 1 = 0
2. Solve for -1/2
3. Set the second factor equal to zero x - 5 = 0
4. Solve for 5
17.
If the solutions to an equation are and , what is the constant term when the equation is written as ?
Answer: -12
Solutions and give factors and . Expanding: . The constant term .