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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

The solutions are z = 5 and z = 9.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

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

Tags

CCSS.8.EE.A.2