Factoring Quadratics

Front

What is factoring in mathematics?

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 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 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

What is the difference of squares?

Back

The difference of squares is a special factoring pattern: a² - b² = (a - b)(a + b).

Front

How do you factor a quadratic expression when a = 1?

Back

When a = 1, factor the expression x² + bx + c by finding two numbers that multiply to c and add to b.

Front

What is the process for factoring a quadratic expression when a ≠ 1?

Back

When a ≠ 1, use the method of grouping or the ac method to factor the expression ax² + bx + c.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as a² + 2ab + b² = (a + b)².

Front

How do you factor the expression 18b² - 9b³?

Back

Factor out the greatest common factor: 9b²(2 - b).