Factoring Quadratics a=1

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of its linear factors.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is (x - p)(x - q) = 0, where p and q are the roots of the equation.

Front

How do you determine the roots of a quadratic equation?

Back

The roots of a quadratic equation can be determined using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

How can you factor a perfect square trinomial?

Back

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

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 7w³ - 14w?

Back

Factor out the common term: 7w(w² - 2).