Trinomials Study Guide

A trinomial is a polynomial with three terms. In general, a trinomial is in the form:

ax^2 + bx + c

Where a, b, and c are constants, and x is the variable.

Factoring Trinomials

To factor a trinomial, you can use different methods such as the AC method, grouping, or trial and error. The goal is to rewrite the trinomial as a product of two binomials.

Example:

Factor the trinomial: x^2 + 5x + 6

We are looking for two numbers that multiply to 6 and add to 5. These numbers are 2 and 3. So, the factored form is:

(x + 2)(x + 3)

Solving Trinomial Equations

To solve trinomial equations, you can use different methods such as factoring, completing the square, or using the quadratic formula.

Example:

Solve the equation: x^2 + 5x + 6 = 0

By factoring, we get:

(x + 2)(x + 3) = 0

So, the solutions are x = -2 and x = -3.

Practice Problems

Now that you understand trinomials, try these practice problems to test your knowledge:

1. Factor the trinomial: x^2 + 7x + 10
2. Solve the equation: x^2 - 4x - 5 = 0
3. Factor the trinomial: 2x^2 + 9x + 7
4. Solve the equation: 3x^2 + 2x - 8 = 0

Once you're done, check your answers and review any concepts you might have struggled with.