Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, 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 is the standard form of a quadratic equation?

Back

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

Front

What does it mean for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as the product of two binomials.

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is written as (px + q)(rx + s), where p, q, r, and s are constants.

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.

Front

How do you factor a perfect square trinomial?

Back

A perfect square trinomial can be factored as (a + b)² or (a - b)², where a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)².

Front

What is the first step in factoring a quadratic expression?

Back

The first step in factoring a quadratic expression is to look for a common factor in all terms.

Front

How do you factor the expression 4x² - 20x + 25?

Back

The expression factors to (2x - 5)².

Front

What is the factored form of x² + 12x + 20?

Back

The expression factors to (x + 2)(x + 10).