Solve by Factoring/Square Roots

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler factors that, when multiplied together, give the original expression.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer.

Front

What does it mean to solve an equation by factoring?

Back

To solve an equation by factoring means to express the equation in a factored form and then set each factor equal to zero to find the solutions.

Front

What is the square root of a number?

Back

The square root of a number is a value that, when multiplied by itself, gives the original number.

Front

How do you solve (x-5)² = 25?

Back

First, take the square root of both sides: x-5 = ±5. Then, solve for x: x = 10 or x = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

What is the relationship between factoring and the quadratic formula?

Back

Factoring can be used to solve quadratic equations, while the quadratic formula provides a method to find the roots when factoring is difficult.

Front

What does it mean if an equation has no real solutions?

Back

An equation has no real solutions if the discriminant (b² - 4ac) is less than zero, indicating that the roots are complex numbers.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root sign, b² - 4ac, which determines the nature of the roots.

Front

How do you check if your solutions to a quadratic equation are correct?

Back

Substitute the solutions back into the original equation to see if they satisfy the equation.