Mathematics
Grade 10
15 min
Solve an equation using the zero product property
Solve an equation using the zero product property
What you'll learn
- Solve addition and subtraction problems with decimals to the hundredths place with at least 80% accuracy.
- Explain the steps for multiplying a decimal by a whole number using place value understanding in their own words.
- Apply the standard algorithm to divide a decimal to the tenths place by a whole number, showing all work, and get the correct quotient at least 7 out of 10 times.
- Identify which operation (addition, subtraction, multiplication, or division) is needed to solve a decimal word problem and justify their choice.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define the Zero Product Property in their own words.
Identify when an equation is in the correct form to apply the Zero Product Property.
Solve quadratic equations that are already in factored form.
Rearrange a quadratic equation into standard form (ax² + bx + c = 0) before solving.
Factor a quadratic expression and then use the Zero Product Property to find the solutions.
Verify the solutions to a quadratic equation by substituting them back into the original equation.
If you multiply two secret numbers together and the answer is zero, what can you say for sure about at least one of those numbers? 🤔
This lesson introduces a powerful shortcut for solving certain equations called the Zero Product Property. You will learn how to use your factoring skills...
2
Key Concepts & Vocabulary
TermDefinitionExample
Zero Product PropertyA rule stating that if the product of two or more factors is zero, then at least one of the factors must be equal to zero.If (x + 2)(x - 3) = 0, then either x + 2 = 0 or x - 3 = 0.
FactorAn algebraic expression that is multiplied with other expressions to form a product.In the expression (x + 5)(x - 1), the factors are (x + 5) and (x - 1).
Factored FormA quadratic expression written as a product of its linear factors.The factored form of x² + 3x - 10 is (x + 5)(x - 2).
RootA value of the variable that makes an equation true. For a quadratic equation, the roots are the x-values where its graph intersects the x-axis.For the equation x² - 9 = 0, the roots are x = 3 and x = -3.
Quadratic EquationAn equation that can be written in the standard form ax...
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Core Formulas
The Zero Product Property
If A \cdot B = 0, then A = 0 \text{ or } B = 0.
Use this rule after you have an equation where one side is a product of factors and the other side is zero. Set each factor equal to zero individually and solve.
Standard Form of a Quadratic Equation
ax^2 + bx + c = 0
Before you can factor and solve, you must rearrange the equation so that all terms are on one side, set equal to zero. This is the required starting format.
5 more steps in this tutorial
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Challenging
A quadratic equation has roots x = -4 and x = 7. Which of the following equations in factored form corresponds to these roots?
A.(x - 4)(x + 7) = 0
B.(x + 4)(x - 7) = 0
C.(x - 4)(x - 7) = 0
D.(x + 4)(x + 7) = 0
Challenging
Solve the equation (x + 1)(x + 2) = 12.
A.x = 2 or x = -5
B.x = 11 or x = 10
C.x = -1 or x = -2
D.x = 3 or x = -4
Challenging
A student's work to solve 2x² + 18x = 0 is shown:
Step 1: 2x² + 18x = 0
Step 2: 2x(x + 9) = 0
Step 3: 2x = 0 or x + 9 = 0
Step 4: x = 2 or x = -9
In which step did the student make the first mistake?
A.Step 1
B.Step 2
C.Step 3
D.Step 4
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Frequently asked questions
What grade level is "Solve an equation using the zero product property"?
Solve an equation using the zero product property is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Solve an equation using the zero product property?
You'll be able to: Solve addition and subtraction problems with decimals to the hundredths place with at least 80% accuracy; Explain the steps for multiplying a decimal by a whole number using place value understanding in their own words; Apply….
Is "Solve an equation using the zero product property" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Solve an equation using the zero product property?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.