Factoring Quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c, 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 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 perfect square trinomial?

Back

A perfect square trinomial can be factored as (a ± b)², where a² and b² are the first and last terms.

Front

What is the difference of squares formula?

Back

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

Front

How do you factor a quadratic expression of the form ax² + bx + c?

Back

To factor ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

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, two 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 terms and factoring out common factors from groups of terms.

Front

What are the steps to factor a quadratic expression completely?

Back

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

Front

What is a linear factor?

Back

A linear factor is an expression of the form (x - r), where r is a root of the polynomial.