QUESTION 24 If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. \( 20 x y+15 \mathrm{by}-16 \mathrm{x}-12 \mathrm{~b} \)

To factor the polynomial \( 20xy + 15by - 16x - 12b \), we can group terms. Let's group \( (20xy + 15by) \) and \( (-16x - 12b) \) together: 1. Factor out the common factors in each group: \( 5y(4x + 3b) - 4(4x + 3b) \). 2. Notice that \( (4x + 3b) \) is a common factor. So we can factor that out: \( (4x + 3b)(5y - 4) \). This final expression is the complete factorization of the polynomial. Here’s a bonus tidbit: Polynomials can look intimidating, but grouping terms is a superhero move in polynomial factoring. It’s like tidying up a messy room by putting your shoes with shoes and your books with books—easy peasy! For a deeper dive, consider exploring polynomial long division or synthetic division. These techniques come in handy when dealing with larger polynomials and can even help uncover hidden factors! They ensure you're not just stopping at what meets the eye.