Factoring Quadratic Trinomials

Front

What is a quadratic trinomial?

Back

A quadratic trinomial is a polynomial of the form ax² + bx + c, where a, b, and c are constants, and a ≠ 0.

Front

What does it mean to factor a quadratic trinomial?

Back

Factoring a quadratic trinomial means expressing it as a product of two binomials.

Front

What is the general form of factoring a quadratic trinomial?

Back

The general form is (x - p)(x - q), where p and q are the roots of the trinomial.

Front

How do you find the roots of a quadratic trinomial?

Back

You can find the roots using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in factoring quadratics?

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 first step in factoring a quadratic trinomial?

Back

The first step is to identify the coefficients a, b, and c in the trinomial.

Front

How can you check if your factorization is correct?

Back

You can check by multiplying the factors back together to see if you obtain the original trinomial.

Front

What is the role of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the shape of the parabola and can influence the method used for factoring.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, such as (x + a)² = x² + 2ax + a².

Front

What is the method of grouping in factoring?

Back

The method of grouping involves rearranging and grouping terms to factor polynomials, often used when there are four terms.