## How to Factor Trinomials

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### The Way to Factor a Trinomial in Three Simple Steps

Being able to factor a trinomial is an exceedingly **vital** and worthwhile skill if you are doing algebra, however, this process may additionally be quite troublesome.

### Definition of Trinomials

Trinomials are polynomials with \(3\) terms. The **first** one is an \(x^2\) term, the **2nd** term is an \(x\) term, and the **3rd** term is a **constant** (merely a number). Trinomial: \(ax^2 \ + \ bx \ + \ c\)

### Factoring Trinomials: a = 1

With this first example, we are going to show the way to **factor** a trinomial whenever \(a\), the **leading** coefficient is \(1\).

### Example one:

Here we are factoring the trinomial: \(x^2 \ + \ 9x \ + \ 14\)

**Step One:** Determine **values** for \(b\) and \(c\). In this case, \(b \ = \ 9\) and \(c \ = \ 14\).

**Step Two:** Locate 2 two numbers which **ADD** to \(b\) and **MULTIPLY** to \(c\). This second step may involve a small amount of **trial** and **error.** For example, you might choose \(4\) and \(5\) since \(4 \ + \ 5 \ = \ 9\). Yet \(4 \times 5\) **doesn’t** come to \(28\), therefore those numbers are no good. But, if we pick \(7\) and \(2\), it is simple to confirm that:

\(7 \ + \ 2 \ = \ 9\) (\(b\)’s value); and \(7 \times 2 \ = \ 14\) (\(c\)’s value)

**Step three:** Utilize the numbers you chose for writing out the factors and **check.** In this case, the factors are \((x \ + \ 7)\) and \((x \ + \ 2)\)**Final** Solution: \((x \ + \ 7)(x \ + \ 2)\)

It is possible to check the answer via **multiplying** the \(2\) factors (binomials) together to find out if the answer is the **original** trinomial like this:

\(x^2 \ + \ 9x \ + \ 14 \ = \ (x \ + \ 7)(x \ + \ 2) \ = \ x^2 \ + \ 7x \ + \ 2x \ + \ 14 \ = \ x^2 \ + \ 9x \ + \ 14\)

If you multiply the factors it **equals** the original trinomial.

### Example two:

Factor the Trinomial: \(x^2 \ + \ 3x \ - \ 18\)

**Step one: **Figure out values for \(b\) and \(c\). With this example, \(b \ = \ 3\) and \(c \ = \ -18\).

**Step two:** Locate \(2\) numbers which **ADD** to \(b\) and **MULTIPLY** to \(c\). Locating the correct numbers will **not** always be as simple as it is with Example one.

In order to make factoring trinomials simpler, jot down every factor of \(c\) you can think of. With this example, \(c \ = \ -18\), therefore:

\(18 \times -1 \ = \ -18, \ 9 \times -2 \ = \ -18, \ 6 \times -3 \ = \ -18, -18 \times 1 \ = \ -18, \ ...\)

Don’t forget that the 2 numbers must **multiply** to \(c\) **AND add** to \(b\). The sole factors of \(-18\) which match **both** those requirements are \(6\) and \(-3\).

**Step three:** Utilize the chosen numbers picked to write out the factors, then and **check**.

The final step is then to write out the factors: \((x \ + \ 6)(x \ - \ 3)\)

\(x^2 \ + \ 3x \ - \ 18 \ = \ (x \ + \ 6)(x \ - \ 3)\)

### Exercises for Factoring Trinomials

**1) **\(2x^2 \ + \ 9x \ - \ 5 = \)

**2) **\(30x^2 \ + \ 14x \ - \ 8 = \)

**3) **\(-24x^2 \ - \ 32x \ - \ 8 = \)

**4) **\(8x^2 \ - \ 7x \ - \ 1 = \)

**5) **\(21x^2 \ + \ 5x \ - \ 4 = \)

**6) **\(-15x^2 \ - \ 37x \ - \ 18 = \)

**7) **\(15x^2 \ - \ 4x \ - \ 4 = \)

**8) **\(-9x^2 \ - \ 36x \ - \ 20 = \)

**9) **\(-9x^2 \ - \ 24x \ - \ 7 = \)

**10) **\( x^2 \ - \ 15 \ x \ + \ 44 \ = \ \)

## Factoring Trinomials Practice Quiz

### More Polynomials courses

- How to Classify Polynomials
- How to Write Polynomials in Standard Form
- How to Multiply Monomials
- How to Simplify Polynomials
- How to Add and Subtract Polynomials
- How to Multiply a Polynomial and a Monomial
- How to Multiply Binomials
- How to Do Operations with Polynomials
- How to Factor Trinomials
- How to Divide Monomials