To factor the trinomial 11m^2 + 14m - 16, we will use the factoring method called "ac method" or "splitting the middle term." Here's how you can do it:
1. Write down the trinomial in the form "am^2 + bm + c" with the coefficients a, b, and c.
In this case, a = 11, b = 14, and c = -16.
2. Multiply the coefficient of the squared term (a) by the constant term (c).
In this case, a * c = 11 * -16 = -176.
3. Find two numbers that multiply to give the result from step 2 (-176) and add up to the coefficient of the middle term (b), which is 14.
In this case, the numbers are -4 and 44, which multiply to -176 and add up to 14.
4. Rewrite the middle term (14m) using the numbers found in step 3 (-4 and 44), splitting it into two terms:
Rewrite 14m as -4m + 44m.
The trinomial becomes 11m^2 - 4m + 44m - 16.
5. Group the terms in pairs:
Rearrange the trinomial by grouping the first two terms together and the last two terms together:
(11m^2 - 4m) + (44m - 16).
6. Factor out the greatest common factor from each group:
Factor out m from the first group and 4 from the second group:
m(11m - 4) + 4(11m - 4).
7. Check if the terms in the parentheses are the same. If they are, you have successfully factored the trinomial.
In this case, both terms are 11m - 4.
The factored form of the trinomial 11m^2 + 14m - 16 is:
(11m - 4)(m + 4).
So, the answer would be (11m - 4)(m + 4), not (11m - 8)(m + 2).