Solving Quadratic Equations by Factoring

What is the zero product property?

• If a product of two expressions is zero, both expressions must be equal.

• If a product of two expressions is zero, one or both of the expressions must be one.

• If a product of two expressions is zero, both expressions must be non-zero.

• If a product of two expressions is zero, one or both of the expressions must be zero.

In the first example, what are the solutions to the equation 2B + 1 = 0 and 3B - 5 = 0?

• B = 1/2 and B = 5/3

• B = -1/2 and B = -5/3

• B = 1/2 and B = -5/3

• B = -1/2 and B = 5/3

What should you do if you make a mistake while solving a quadratic equation?

• Change the equation.

• Ask someone else to solve it for you.

• Review the mistake to understand what went wrong.

• Ignore the mistake and move on.

In the second example, what are the solutions to the equation 4N - 1 = 0 and 7N + 1 = 0?

• N = 1/4 and N = -1/7

• N = -1/4 and N = 1/7

• N = 1/4 and N = 1/7

• N = -1/4 and N = -1/7

What is the first step in solving a quadratic equation that is not factored?

• Divide both sides by the same number.

• Add the same number to both sides.

• Multiply both sides by zero.

• Ensure one side of the equation equals zero.

In the third example, what are the solutions to the equation X + 3 = 0 and X + 4 = 0?

• X = 3 and X = -4

• X = -3 and X = 4

• X = 3 and X = 4

• X = -3 and X = -4

Why is it important to have zero on one side of the equation when using the zero product property?

• Because it makes the equation easier to read.

• Because the property only applies when the product is zero.

• Because it is a rule in algebra.

• Because it simplifies the equation.

In the fourth example, what are the solutions to the equation 2K + 5 = 0 and K - 1 = 0?

• K = -5/2 and K = 1

• K = 5/2 and K = -1

• K = -5/2 and K = -1

• K = 5/2 and K = 1

What is the purpose of creating a box when factoring a quadratic equation?

• To subtract the terms.

• To divide the terms.

• To organize the terms and find the greatest common factor.

• To add the terms together.

In the final example, what are the solutions to the equation 3K - 5 = 0 and K - 1 = 0?

• K = 5/3 and K = 1

• K = -5/3 and K = -1

• K = 5/3 and K = -1

• K = -5/3 and K = 1