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

Textbook Question

Chapter 5, 5.2 - Problem 30 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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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)`

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Factor out the greatest common factors:

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

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Put the numbers outside in a parentheses together :

(b - 3) (b+9)

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and that's the factored form of the problem.

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taangerine | Student, Grade 12 | (Level 1) Valedictorian

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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. 

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