Mathematics
Grade 10
15 min
Solve a quadratic equation by factoring
Solve a quadratic equation by factoring
What you'll learn
- Solve multi-step word problems involving addition, subtraction, multiplication, and division of whole numbers, showing all work and steps clearly.
- Explain the order of operations (PEMDAS/BODMAS) and apply it correctly to solve equations with multiple operations.
- Multiply multi-digit whole numbers using the standard algorithm with at least 80% accuracy on a worksheet.
- Divide multi-digit whole numbers by two-digit divisors using long division, showing the quotient and remainder.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify and write a quadratic equation in standard form.
Explain and apply the Zero Product Property to solve equations.
Factor quadratic trinomials where the leading coefficient is 1.
Factor quadratic trinomials where the leading coefficient is greater than 1.
Solve quadratic equations involving special cases, such as a difference of squares or a greatest common factor.
Verify the solutions (roots) of a quadratic equation by substituting them back into the original equation.
If you throw a basketball, how can you predict the exact moment it hits the ground? 🏀 The answer lies in solving a quadratic equation!
This tutorial will teach you a powerful algebraic method to solve quadratic equations: factoring. You will learn how to break down complex equatio...
2
Key Concepts & Vocabulary
TermDefinitionExample
Quadratic EquationAn equation that can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants and 'a' is not equal to zero. Its graph is a parabola.x² - 3x + 2 = 0 is a quadratic equation where a=1, b=-3, and c=2.
Standard FormThe form ax² + bx + c = 0. It is essential to arrange the equation in this form before you begin factoring.The equation 5x = 6 - 2x² is written in standard form as 2x² + 5x - 6 = 0.
FactoringThe process of breaking down a polynomial into a product of simpler polynomials (its factors).The quadratic expression x² + 5x + 6 can be factored into (x + 2)(x + 3).
Zero Product PropertyA fundamental rule stating that if the product of two or more factors is zero, then at least one of the factors must be zero.If (x +...
3
Core Formulas
Standard Form of a Quadratic Equation
ax^2 + bx + c = 0
Before solving, you must arrange the equation so that all terms are on one side, set equal to zero. The term with x² should ideally have a positive coefficient 'a'.
The Zero Product Property
If A \cdot B = 0, then A = 0 \text{ or } B = 0
This is the core principle for solving by factoring. Once the quadratic is factored into a product of binomials, set each binomial factor equal to zero and solve for the variable.
Difference of Squares
a^2 - b^2 = (a - b)(a + b)
A common factoring pattern to recognize when a quadratic has two terms that are perfect squares separated by a subtraction sign.
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
Solve for x: 6x² + 5x - 4 = 0.
A.x = 1/2, x = -4/3
B.x = -1/2, x = 4/3
C.x = 2, x = -2/3
D.x = -2, x = 2/3
Challenging
What is the sum of the roots of the equation 2x² - 14x - 36 = 0?
A.-7
B.7
C.18
D.-18
Challenging
For a variable k, what are the solutions to the equation x² + (k - 3)x - 3k = 0?
A.x = 3, x = k
B.x = -3, x = k
C.x = 3, x = -k
D.x = -3, x = -k
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Quadratic equations
Mathematics for other grades
Frequently asked questions
What grade level is "Solve a quadratic equation by factoring"?
Solve a quadratic equation by factoring is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Solve a quadratic equation by factoring?
You'll be able to: Solve multi-step word problems involving addition, subtraction, multiplication, and division of whole numbers, showing all work and steps clearly; Explain the order of operations (PEMDAS/BODMAS) and apply it correctly to solve….
Is "Solve a quadratic equation by factoring" 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 a quadratic equation by factoring?
This lesson includes 24 practice questions across multiple difficulty levels, each with instant feedback and explanations.