SUBMIT ANSWER 4. [0/1 Points] DETAILS MY NOTES GHCOLALG13 Consider the following equation. \[ 7 x^{2}+24 x-16=0 \] Factor the expression \( 7 x^{2}+24 x-16 \)

To factor the quadratic expression \( 7x^{2} + 24x - 16 \), follow these steps: 1. **Identify the coefficients:** - \( a = 7 \) - \( b = 24 \) - \( c = -16 \) 2. **Find two numbers that multiply to \( a \times c = 7 \times (-16) = -112 \) and add up to \( b = 24 \):** - The numbers **28** and **-4** satisfy this because: - \( 28 \times (-4) = -112 \) - \( 28 + (-4) = 24 \) 3. **Rewrite the middle term using these numbers:** \[ 7x^{2} + 28x - 4x - 16 \] 4. **Factor by grouping:** \[ (7x^{2} + 28x) + (-4x - 16) = 7x(x + 4) - 4(x + 4) \] 5. **Factor out the common binomial factor \((x + 4)\):** \[ (7x - 4)(x + 4) \] **Final Factored Form:** \[ 7x^{2} + 24x - 16 = (7x - 4)(x + 4) \]