Solving Quadratics by Factoring

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

Back

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

Front

What is the Zero-Product Property?

Back

The Zero-Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, first factor the quadratic into two binomials, set each factor equal to zero, and solve for the variable.

Front

What are the steps to factor the quadratic x² + 4x - 32?

Back

1. Find two numbers that multiply to -32 and add to 4. 2. The numbers are 8 and -4. 3. Factor: (x + 8)(x - 4) = 0.

Front

What are the solutions to the equation x² + 4x - 32 = 0?

Back

The solutions are x = -8 and x = 4.

Front

What is the significance of the numbers chosen when factoring a quadratic?

Back

The numbers chosen when factoring are the roots of the equation, not the solutions. They help in forming the binomials.

Front

How do you factor the quadratic z² - 14z + 45?

Back

1. Find two numbers that multiply to 45 and add to -14. 2. The numbers are -5 and -9. 3. Factor: (z - 5)(z - 9) = 0.

Front

What are the solutions to the equation z² - 14z + 45 = 0?

Back

The solutions are z = 5 and z = 9.

Front

What is the process to solve k² - 6 = 43?

Back

1. Rearrange to k² = 49. 2. Take the square root: k = ±7.