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Name: Date: Solving Quadratics by Factoring Out Section I. Find the zeros of each equation. 1. 4! ! 8! 0 3. ! ! + 5! 0 5. 27! ! 9! 0 7. 24! ! 20! 0 9

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How to fill out solving quadratics by factoring:

1. Identify the quadratic equation: The first step in solving quadratics by factoring is to identify the equation you want to solve. Quadratic equations have the form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.
2. Set the equation equal to zero: To factor the quadratic equation, it needs to be set equal to zero. This is done by subtracting the constant term, c, from both sides of the equation.
3. Factor the equation: Now, you need to factor the quadratic equation. Look for common factors among the coefficients a, b, and c. If there are common factors, factor them out first. Then, try to find two binomial expressions that can multiply together to give the original quadratic equation.
4. Set each factor equal to zero: Once you have factored the quadratic equation, set each factor equal to zero. This is because the product of two factors equals zero only if at least one of the factors is zero.
5. Solve for x: Solve each of the resulting equations obtained from setting the factors equal to zero. This will give you the values of x that make the quadratic equation true.

Who needs solving quadratics by factoring:

1. Students studying algebra: Solving quadratics by factoring is an important concept in algebra. It helps students understand the relationship between factors and zeroes of quadratic equations.
2. Engineers and scientists: Quadratic equations are frequently used in engineering and scientific fields for modeling physical phenomena. Being able to factor quadratics is essential for analyzing and solving these mathematical models.
3. Problem solvers: Factoring quadratics can be a valuable problem-solving technique in various contexts. It allows individuals to find solutions to real-life problems involving the relationship between two variables.

In conclusion, solving quadratics by factoring involves identifying the quadratic equation, setting it equal to zero, factoring the equation, setting each factor equal to zero, and solving for x. This method is useful for students studying algebra, engineers and scientists, as well as problem solvers in various fields.

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