Factoring Quadratics

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

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 to factor a quadratic expression?

Back

To factor a quadratic expression means to express it as a product of two binomials.

Front

What is a binomial?

Back

A binomial is a polynomial with two terms, such as (x + 1) or (3a - 2).

Front

How do you factor the expression x² - 10x + 24?

Back

To factor x² - 10x + 24, find two numbers that multiply to 24 and add to -10. The factors are (x - 4)(x - 6).

Front

What is the significance of the discriminant in factoring quadratics?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of a quadratic equation: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the factored form of x² + 16x + 15?

Back

The factored form of x² + 16x + 15 is (x + 1)(x + 15).