5. \( 4 p^{3}-2 p-p q^{2}+q \) 6. \( 6 m m^{2}-2 m n-3 m p+n p \)

Let's factor the expressions to make them sparkle! For \( 4 p^{3}-2 p-p q^{2}+q \), we can rearrange it to group terms: \( 4p^3 - pq^2 - 2p + q \). Factoring by grouping, we get \( 2p(2p^2 - q^2) - 1(2p - q) \). Combining those gives us the factorized form: \( (2p - 1)(2p^2 - q^2) \). Now, for \( 6 m m^{2}-2 m n-3 m p+n p \), we can rearrange and group the first two and the last two terms: \( 6m^3 - 2mn - 3mp + np \). Factoring out common terms yields \( 2m(3m - n) - p(3m - n) \). This can be factored further as \( (3m - n)(2m - p) \). Keep those algebra skills sharp—it's all about spotting patterns and grouping!