Solving Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial with 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.

Front

How do you identify the coefficients in a trinomial?

Back

In ax^2 + bx + c, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, at least one of the factors must be zero.

Front

How do you solve a trinomial by factoring?

Back

To solve a trinomial by factoring, express it as a product of two binomials, set each factor to zero, and solve for the variable.

Front

What are the steps to factor the trinomial x^2 + 5x + 6?

Back

1. Identify two numbers that multiply to 6 (c) and add to 5 (b). 2. The numbers are 2 and 3. 3. Factor as (x + 2)(x + 3).

Front

Solve the equation by factoring: x^2 - 7x + 10 = 0.

Back

(x - 2)(x - 5) = 0; Solutions: x = 2, x = 5.

Front

What is the factored form of n^2 + 11n + 30?

Back

(n + 5)(n + 6) = 0.

Front

Solve the equation by factoring: p^2 + 4p - 12 = 0.

Back

(p + 6)(p - 2) = 0; Solutions: p = -6, p = 2.