Quad. Factoring

Front

What is factoring in algebra?

Back

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

Front

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.

Front

What are the solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called the roots or zeros of the equation.

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots using factoring, completing the square, or the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

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.

Front

What does it mean for a quadratic to be factored?

Back

Factoring a quadratic means expressing it as a product of two binomials, such as (x - p)(x - q), where p and q are the roots.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

Factor the expression: x² + 5x - 24

Back

(x + 8)(x - 3)

Front

Factor the expression: x² - 10x - 24

Back

(x - 12)(x + 2)

Front

Factor the expression: 2m² + 3m - 9

Back

(m + 3)(2m - 3)