Factoring Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax² + bx + c.

Front

What does it mean to factor a trinomial?

Back

Factoring a trinomial involves rewriting it as a product of two binomials.

Front

What is the general form of factoring a trinomial of the form ax² + bx + c?

Back

The general form is (px + q)(rx + s) where p, q, r, and s are constants.

Front

How do you identify the coefficients in a trinomial?

Back

In the trinomial ax² + bx + c, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the first step in factoring a trinomial?

Back

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

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b² - 4ac) helps determine the nature of the roots of the trinomial; if it's a perfect square, the trinomial can be factored into rational numbers.

Front

What is the method of grouping in factoring?

Back

The method of grouping involves rearranging and grouping terms to factor by pairs.

Front

How can you factor a trinomial when a = 1?

Back

When a = 1, you look for two numbers that multiply to c and add to b.

Front

What is the FOIL method in relation to factoring?

Back

The FOIL method (First, Outside, Inside, Last) is used to multiply two binomials and can help in reverse engineering the factors.

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 (a + b)² = a² + 2ab + b².