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

2 Answers

Educator Approved

Educator Approved
tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

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)

Educator Approved

Educator Approved
atyourservice's profile pic

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

Posted on

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`

` `

now group:

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

` `

Factor out the greatest common factors:

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

` `

Put the numbers outside in a parentheses together :

(11m - 8) (m + 2)

` `

This is the factored version of the equation.