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 are the factors of a quadratic expression?

Back

The factors of a quadratic expression are the binomials that multiply together to produce the quadratic expression.

Front

What is the standard form of a quadratic equation?

Back

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

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 two numbers.

Front

What is the difference of squares?

Back

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

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 when a ≠ 1?

Back

When a ≠ 1, use the method of grouping or the ac method: multiply a and c, find two numbers that multiply to ac and add to b, then rewrite the expression and factor by grouping.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² ± 2ab + b², which factors to (a ± b)².

Front

What is the role of the leading coefficient in factoring quadratics?

Back

The leading coefficient (a) affects the shape of the parabola and can complicate factoring; it may require special techniques if not equal to 1.