\#1/16 Multiplying Polynomials \( (n-5)(3 n-4) \) \( 3 n^{2}-19 n+20 \) \( 3 n^{2}-19 n-20 \) \( 3 n^{2}+19 n-20 \) \( 3 n^{2}-11 n+20 \)

To multiply the polynomials \( (n-5)(3n-4) \), you can apply the distributive property, also known as the FOIL method for binomials. Multiply each term in the first polynomial by each term in the second polynomial: 1. \( n \times 3n = 3n^2 \) 2. \( n \times -4 = -4n \) 3. \( -5 \times 3n = -15n \) 4. \( -5 \times -4 = 20 \) Now, combine the like terms: \( 3n^2 - 4n - 15n + 20 = 3n^2 - 19n + 20 \). So, the correct answer is \( 3n^2 - 19n + 20 \). Consider this multiplication just like a recipe; you have the ingredients from both polynomials, and by mixing them just right, you achieve the perfect dish – in this case, a new polynomial! Have fun with it, and you’ll find multiplying polynomials can be quite satisfying. Next time you're grappling with polynomials, remember to keep your work organized. Common mistakes involve signs or misaligning terms. When multiplying, it's easy to write \( -4n + -15n \) as \( -19n \) but don’t forget to keep your attention sharp—this is where the fun lies! Always double-check your work for the right combination of terms.