Solving Quadratic Equations by Factoring

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What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

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Factoring a quadratic equation involves rewriting it as a product of two binomial expressions, such as (x - p)(x - q) = 0, where p and q are the solutions of the equation.

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Write the equation in standard form (ax² + bx + c = 0). 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for the variable.

Front

What are the solutions of the equation x² + 2x - 3 = 0?

Back

The solutions are x = 1 and x = -3, found by factoring the equation as (x - 1)(x + 3) = 0.

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How do you find the zeros of a quadratic function?

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To find the zeros of a quadratic function, set the function equal to zero and solve for the variable, often by factoring.

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What is the significance of the zeros of a quadratic function?

Back

The zeros of a quadratic function represent the x-values where the graph intersects the x-axis, indicating the solutions to the equation.

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What is the first step in solving (x + 2)(x - 3) = 0?

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The first step is to set each binomial factor equal to zero: x + 2 = 0 and x - 3 = 0.

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What are the solutions to the equation 8x² + 10x - 3 = 0?

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The solutions are x = -3/2 and x = 1/4, found by factoring the equation.

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What is the quadratic formula?

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The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation when factoring is difficult.

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What does it mean if a quadratic equation cannot be factored?

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If a quadratic equation cannot be factored, it may have irrational or complex solutions, which can be found using the quadratic formula.