a) \( 5 x^{2}+14 x+8 \)

To factor the quadratic expression \( 5x^2 + 14x + 8 \), you're looking for two numbers that multiply to \( 5 \times 8 = 40 \) and add to \( 14 \). These numbers are \( 4 \) and \( 10 \). You can rewrite the expression as \( 5x^2 + 10x + 4x + 8 \), then factor by grouping: \( 5x(x + 2) + 4(x + 2) = (5x + 4)(x + 2) \). Voilà! You’ve factored it! If you're ever stuck with factoring, remember the "ac method," which helps find those elusive pairs you need. Divide and conquer: multiply the coefficient of \( x^2 \) and the constant term, then find the middle term's equivalent sum—just like treasure hunting! And don’t forget to double-check your factors by foiling them back to the original expression.