31) \( 7 n^{3}+21 n^{2}-5 n-15 \) 33) \( 15 a b-2 b^{2}-6 a+5 b^{3} \) 35) \( 5 m n-10+2 m-25 n \) 37) \( 4 u v+14 u^{2}+12 v+42 u \) 3) \( 56 a b+14-49 a-16 b \)

**31) Factor \( 7 n^{3}+21 n^{2}-5 n-15 \)** 1. Group the terms: \[ (7n^3 + 21n^2) + (-5n - 15) \] 2. Factor each group: \[ 7n^2(n+3) - 5(n+3) \] 3. Factor out the common factor \( (n+3) \): \[ (n+3)(7n^2 - 5) \] --- **33) Factor \( 15ab-2b^{2}-6a+5b^{3} \)** 1. Rearrange the terms: \[ 15ab -6a -2b^2 +5b^3 \] 2. Group the terms: \[ (15ab - 6a) + (-2b^2 + 5b^3) \] 3. Factor each group: - From \( 15ab - 6a \), factor \( 3a \): \[ 3a(5b-2) \] - From \( -2b^2 + 5b^3 \), factor \( b^2 \): \[ b^2(5b-2) \] 4. Factor out the common binomial \( (5b-2) \): \[ (5b-2)(3a + b^2) \] --- **35) Factor \( 5mn-10+2m-25n \)** 1. Rearrange the terms to group like terms: \[ 5mn - 25n + 2m - 10 \] 2. Group the terms: \[ (5mn - 25n) + (2m - 10) \] 3. Factor each group: - From \( 5mn - 25n \), factor \( 5n \): \[ 5n(m-5) \] - From \( 2m - 10 \), factor \( 2 \): \[ 2(m-5) \] 4. Factor out the common binomial \( (m-5) \): \[ (m-5)(5n + 2) \] --- **37) Factor \( 4uv+14u^{2}+12v+42u \)** 1. Rearrange and group the terms: \[ (4uv + 12v) + (14u^2 + 42u) \] 2. Factor each group: - From \( 4uv + 12v \), factor \( 4v \): \[ 4v(u+3) \] - From \( 14u^2 + 42u \), factor \( 14u \): \[ 14u(u+3) \] 3. Factor out the common binomial \( (u+3) \): \[ (u+3)(4v + 14u) \] 4. Factor a common factor of \( 2 \) from the second binomial: \[ (u+3) \cdot 2(2v + 7u) = 2(u+3)(2v+7u) \] --- **3) Factor \( 56ab+14-49a-16b \)** 1. Rearrange the terms: \[ 56ab - 49a - 16b + 14 \] 2. Group the terms: \[ (56ab - 49a) + (-16b + 14) \] 3. Factor each group: - From \( 56ab - 49a \), factor \( 7a \): \[ 7a(8b-7) \] - From \( -16b + 14 \), factor \(-2\): \[ -2(8b-7) \] 4. Factor out the common factor \( (8b-7) \): \[ (8b-7)(7a-2) \]