`8x^2 + 18x + 9` Factor the trinomial. If the trinomial cannot be factored, say so.

Textbook Question

Chapter 5, 5.2 - Problem 37 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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We can solve this using the AC factoring method:

8x^2 + 18x + 9

Multiply a by c

8 x 9 = 72

Find factors of 72 that add up to b (18)

12 and 6 meet the requirement, plug these in as b

8x^2 + 12x + 6x + 9

now group:

(8x^2 + 12x) + (6x + 9)

Factor out the greatest common factors:

4x (2x + 3 ) + 3 (2x + 3)

Put the numbers outside in a parentheses together :

(4x + 3) (2x + 3)

is the factored form.

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