Solving Quadratic Equations by Factoring
Solve quadratic equations by factoring the polynomial, applying the Zero Product Property, and solving each factor. Master Grade 9 factoring-based quadratic solutions.
Key Concepts
Property To solve a quadratic equation, write it in standard form, $ax^2 + bx + c = 0$. Then, factor the quadratic expression and use the Zero Product Property to find the roots.
Explanation First, get all terms to one side so your equation equals zero. Next, factor the polynomial into smaller pieces. Finally, set each piece equal to zero and solve. This three step method turns a tricky quadratic into simple mini problems that are way easier to crack.
Examples To solve $x^2 + 4x = 12$, first write it as $x^2 + 4x 12 = 0$. Then factor to get $(x+6)(x 2)=0$. The roots are $x= 6$ and $x=2$. To solve $5x^2 2 = 3x$, rewrite as $5x^2 3x 2 = 0$. Then factor to get $(5x+2)(x 1)=0$. The roots are $x= \frac{2}{5}$ and $x=1$.
Common Questions
What are the key steps to solving quadratic equations by factoring?
Identify the equation type, isolate the variable using inverse operations, and verify by substituting back into the original equation.
What common mistakes occur when solving quadratic equations by factoring?
Applying operations to only one side, sign errors when moving terms, and not checking solutions in the original equation.
How is this skill applied in real problems?
These techniques model physical, financial, and geometric situations where unknown quantities must be found from given conditions.