Trinomials

A trinomial is a polynomial with three terms. It is in the form:

ax² + bx + c

where a, b, and c are constants, and a ≠ 0.

Factoring Trinomials

To factor a trinomial, you can use various methods such as:

1. Factoring by Grouping: This method involves grouping the terms of the trinomial in pairs and factoring each pair separately.
2. Factoring by Trial and Error: This method involves finding the pairs of numbers that multiply to give the constant term 'c' and add to give the coefficient of the middle term 'b'.
3. Factoring with the Quadratic Formula: If the trinomial cannot be factored using the above methods, the quadratic formula can be used to find the roots of the trinomial.

Example:

Factor the trinomial: 2x² + 7x + 3

We can use the factoring by grouping method:

2x² + 6x + x + 3

2x(x + 3) + 1(x + 3)

(2x + 1)(x + 3)

Practice Problems:

1. Factor the trinomial: 3x² - 4x - 4
2. Factor the trinomial: 5x² + 11x + 2
3. Factor the trinomial: x² - 5x + 6

Solution:

1. 3x² - 6x + 2x - 4 = 3x(x - 2) + 2(x - 2) = (3x + 2)(x - 2)
2. 5x² + 10x + x + 2 = 5x(x + 2) + 1(x + 2) = (5x + 1)(x + 2)
3. x² - 3x - 2x + 6 = x(x - 3) - 2(x - 3) = (x - 3)(x - 2)

Summary

In summary, trinomials are polynomials with three terms, and they can be factored using various methods such as factoring by grouping, trial and error, or the quadratic formula. Practice factoring trinomials to become more proficient in this skill.