\( 11 \mathrm{~m}^{2}+86 m-16=\square \) (Type your answer in factored form.)

To factor the quadratic expression \( 11m^2 + 86m - 16 \), follow these steps: 1. **Identify the coefficients:** - \( a = 11 \) - \( b = 86 \) - \( c = -16 \) 2. **Find two numbers that multiply to \( a \times c = 11 \times (-16) = -176 \) and add up to \( b = 86 \).** - The numbers **88** and **-2** satisfy this condition because: - \( 88 \times (-2) = -176 \) - \( 88 + (-2) = 86 \) 3. **Rewrite the middle term using these numbers:** \[ 11m^2 + 88m - 2m - 16 \] 4. **Factor by grouping:** \[ (11m^2 + 88m) + (-2m - 16) = 11m(m + 8) - 2(m + 8) \] 5. **Factor out the common binomial factor \((m + 8)\):** \[ (m + 8)(11m - 2) \] **Final Factored Form:** \[ (11m - 2)(m + 8) \] **Answer:** \((11m - 2)(m + 8)\)