Faltorise \( 5 x^{2}+28 x+15 \)

To factorize the quadratic expression \( 5x^2 + 28x + 15 \), follow these steps: 1. **Identify the coefficients:** - \( a = 5 \) (coefficient of \( x^2 \)) - \( b = 28 \) (coefficient of \( x \)) - \( c = 15 \) (constant term) 2. **Find two numbers that multiply to \( a \times c = 5 \times 15 = 75 \) and add up to \( b = 28 \):** - The numbers are **3** and **25** because: - \( 3 \times 25 = 75 \) - \( 3 + 25 = 28 \) 3. **Rewrite the middle term using these numbers:** \[ 5x^2 + 3x + 25x + 15 \] 4. **Factor by grouping:** \[ (5x^2 + 3x) + (25x + 15) \] \[ x(5x + 3) + 5(5x + 3) \] 5. **Factor out the common binomial factor \((5x + 3)\):** \[ (x + 5)(5x + 3) \] **Final Factorized Form:** \[ 5x^2 + 28x + 15 = (x + 5)(5x + 3) \]