# `b^2 + 6b - 27` Factor the trinomial. If the trinomial cannot be factored, say so.

*print*Print*list*Cite

### 2 Answers

Taangerine's method is one way to find the solution.

Another way to work it out would be using the AC factoring method:

`b^2 +6b - 27`

Multiply a by c

1 x -27

Find factors of -27 that add up to b (6)

these numbers will be 9 and -3, plug these in as b

`b^2 + 9b - 3b - 27`

now group:

`(b^2 + 9b)( - 3b - 27)`

` `

Factor out the greatest common factors:

b(b + 9) -3 (b + 9)

` `

Put the numbers outside in a parentheses together :

(b - 3) (b+9)

` `

and that's the factored form of the problem.

Usually, using the quadratic equation to factor the trinomial is one method to get your answer.

1. First, let's identify the a, b, and c in trinomial.

- a=1
- b=-6
- c=-27

2. Using the quadratic equation: `x=(-b+sqrt(b^(2)-4ac))/(2a) and x=(-b-sqrt(b^(2)-4ac))/(2a)` , plug in a, b, and c. ` `

- `x=(6+sqrt(-6^(2)-4(1)(-27)))/(2(1))`
- `x=(6-sqrt(-6^(2)-4(1)(-27)))/(2(1))`

3. Simplify.

- `x=(6+sqrt(-6^(2)-4(1)(-27)))/(2(1))=9`
- `x=(6-sqrt(6^(2)-4(1)(-27)))/(2(1))=-3`

Your solution is 9 and -3. Therefore your answer is **(x+9)(x-3)**.

**CHECK:** (Using FOIL method -- First, Outside, Inside, Last)

*1. Expand (x+9)(x-3)*

- `x^(2)-3x+9x-27`

*2. Simplify, Combine like terms*

*`x^(2)+6x-27`*

*Since your answer is the same as the original equation given, you know that you factored correctly. *

- ` `
- ` `