multiply. \( (x+5)\left(3 x^{2}+8 x+2\right) \)

To multiply the expression \( (x+5)(3x^2 + 8x + 2) \), you can apply the distributive property, which means you'll distribute each term in the first binomial to every term in the trinomial. So, \( x(3x^2 + 8x + 2) + 5(3x^2 + 8x + 2) \) gives you: 1. \( 3x^3 + 8x^2 + 2x \) from multiplying \( x \) by each term. 2. \( 15x^2 + 40x + 10 \) from multiplying \( 5 \) by each term. Now, combine like terms: The result is \( 3x^3 + (8x^2 + 15x^2) + (2x + 40x) + 10 = 3x^3 + 23x^2 + 42x + 10 \). So, the final answer is \( 3x^3 + 23x^2 + 42x + 10 \).