Factoring Quadratics

Front

What is factoring in mathematics?

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 expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What does it mean for an expression to be factorable?

Back

An expression is factorable if it can be expressed as a product of two or more simpler expressions.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 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.

Front

How do you factor a quadratic expression of the form x² + bx + c?

Back

To factor x² + bx + c, find two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n), where m and n are those numbers.

Front

What are the factors of x² - 9?

Back

The factors of x² - 9 are (x - 3)(x + 3), which is a difference of squares.

Front

What is the process to factor a quadratic expression like 4x² - 16x - 9?

Back

To factor 4x² - 16x - 9, look for two numbers that multiply to (4 * -9) = -36 and add to -16. The factors are (2x - 9)(2x + 1).

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

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, set the equation to zero, factor the quadratic, and then set each factor equal to zero to find the solutions.