`11m^2 + 14m - 16` Factor the trinomial. If the trinomial cannot be factored, say so.

Textbook Question

Chapter 5, 5.2 - Problem 42 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The trinomial 11m^2 + 14m - 16 has to be factored.

To do this express 14 as a sum of two two numbers a and b such that a*b = 11*-16 = -176

14 = 22 - 8 and 22*-8 = -176

11m^2 + 14m - 16

= 11m^2 + 22m - 8m - 16

= 11m(m + 2) - 8(m+2)

= (11m - 8)(m+2)

The factored form of 11m^2 + 14m - 16 is (11m - 8)(m+2)

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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We can solve this using the AC factoring method:

`11m^2 + 14m - 16`

Multiply a by c

11 x -16 = -176

Find factors of -176 that add up to b (14)

these numbers will be -8 and 22, plug these in as b

`11m^2 + 22m - 8m - 16`

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now group:

`(11m^2 + 22m) -( 8m - 16)`

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Factor out the greatest common factors:

`11m(m + 2) - 8 (m + 2)`

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Put the numbers outside in a parentheses together :

(11m - 8) (m + 2)

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This is the factored version of the equation.

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