Factoring Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form of ax^2 + 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 standard form of a quadratic equation?

Back

The standard form is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the relationship between the roots of a trinomial and its factors?

Back

The roots of a trinomial are the values of x that make the trinomial equal to zero, and they correspond to the values that make each factor equal to zero.

Front

How do you factor the trinomial x^2 + 5x + 6?

Back

The factors are (x + 2)(x + 3).

Front

What is the first step in factoring a trinomial?

Back

Identify the coefficients a, b, and c in the trinomial ax^2 + bx + c.

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b^2 - 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

How do you factor k^2 - 2k - 24?

Back

The factors are (k - 6)(k + 4).

Front

What is a binomial?

Back

A binomial is a polynomial with two terms, such as (x + 3) or (k - 5).

Front

What is the FOIL method?

Back

FOIL stands for First, Outside, Inside, Last; it's a method used to multiply two binomials.