Factoring Quadratics

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.

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

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ .

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

The zero-product property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ .

To factor $$x^2 + bx + c$$ , find two numbers that multiply to c and add to b, then express it as $$(x + m)(x + n)$$ where m and n are the two numbers.

The difference of squares is a special factoring pattern that states $$a^2 - b^2 = (a - b)(a + b)$$ .

A perfect square trinomial can be factored as $$(a + b)^2 = a^2 + 2ab + b^2$$ or $$(a - b)^2 = a^2 - 2ab + b^2$$ .

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

A quadratic expression is considered prime if it cannot be factored into the product of two binomials with real coefficients.