Factoring Trinomials (a=1)

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form 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 of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the relationship between the coefficients and the roots of a trinomial?

Back

The sum of the roots is equal to -b/a and the product of the roots is equal to c/a.

Front

How do you factor the trinomial x^2 - 16x + 48?

Back

You can factor it as (x - 12)(x - 4).

Front

What is the first step in factoring a trinomial?

Back

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

Front

What is the significance of the discriminant in factoring quadratics?

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 the trinomial m^2 - 13m + 40?

Back

You can factor it as (m - 5)(m - 8).

Front

What is the method to factor a trinomial when a = 1?

Back

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

Front

How do you factor the trinomial r^2 - 16r + 60?

Back

You can factor it as (r - 6)(r - 10).