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 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 is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

When a = 1, you look for two numbers that multiply to c and add to b, then write the expression as (x + m)(x + n), where m and n are the two numbers.

Front

What is the process for factoring a quadratic expression when a ≠ 1?

Back

When a ≠ 1, you can use the 'ac method': multiply a and c, find two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the factored form of the expression 2x² + 5x + 3?

Back

The factored form is (2x + 3)(x + 1).

Front

How can you check if your factorization is correct?

Back

You can check your factorization by multiplying the factors back together to see if you obtain the original quadratic expression.

Front

What is a perfect square trinomial?

Back

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

Front

What is the factored form of the expression 3x² - 12?

Back

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