Factoring Quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard 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 two binomials.

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 are the steps to factor a quadratic expression?

Back

1. Identify a, b, and c from the quadratic expression. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the expression using these numbers. 4. Factor by grouping.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, e.g., (a + b)² = a² + 2ab + b².

Front

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

Back

When a ≠ 1, use the method of grouping or the AC method, where you multiply a and c, find factors of that product that add to b, and then group the terms.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What is the factored form of the quadratic expression x² - 5x + 6?

Back

The factored form is (x - 2)(x - 3).

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

The sum of the roots is -b/a and the product of the roots is c/a, according to Vieta's formulas.

Front

How can you check if your factored form is correct?

Back

You can check by expanding the factored form to see if it equals the original quadratic expression.