1. Factor the polynomial $wp + 2n + 8p + 16$. 2. Factor the polynomial $3bc - 2b - 10 + 15c$. 3. Factor the polynomial $3km - 21k + 2m - 14$. 4. Factor the polynomial $10p^2q - 5p^4 + 3pq - 6q^2$. --- ### Problem 1: Factor $wp + 2n + 8p + 16$ 1. Group terms: $(wp + 8p) + (2n + 16)$ 2. Factor out common factors: $$p(w + 8) + 2(n + 8)$$ 3. Notice no common binomial factor, so this is the factored form. --- ### Problem 2: Factor $3bc - 2b - 10 + 15c$ 1. Group terms: $(3bc + 15c) + (-2b - 10)$ 2. Factor out common factors: $$3c(b + 5) - 2(b + 5)$$ 3. Factor out common binomial: $$\cancel{(b + 5)}(3c - 2)$$ 4. Final factored form: $$(b + 5)(3c - 2)$$ --- ### Problem 3: Factor $3km - 21k + 2m - 14$ 1. Group terms: $(3km - 21k) + (2m - 14)$ 2. Factor out common factors: $$3k(m - 7) + 2(m - 7)$$ 3. Factor out common binomial: $$\cancel{(m - 7)}(3k + 2)$$ 4. Final factored form: $$(m - 7)(3k + 2)$$ --- ### Problem 4: Factor $10p^2q - 5p^4 + 3pq - 6q^2$ 1. Group terms: $(10p^2q - 5p^4) + (3pq - 6q^2)$ 2. Factor out common factors: $$5p^2(q - p^2) + 3q(p - 2q)$$ 3. Notice the binomials are different, try rearranging or factoring by grouping differently. Try grouping as $(10p^2q + 3pq) + (-5p^4 - 6q^2)$ 4. Factor out common factors: $$pq(10p + 3) - 1(5p^4 + 6q^2)$$ No common binomial factor. 5. Try factoring as two separate parts: - $10p^2q - 5p^4 = 5p^2(2q - p^2)$ - $3pq - 6q^2 = 3q(p - 2q)$ No common binomial factor. 6. Since no common binomial factor, the expression is factored as: $$5p^2(2q - p^2) + 3q(p - 2q)$$ --- **Final answers:** 1. $p(w + 8) + 2(n + 8)$ 2. $(b + 5)(3c - 2)$ 3. $(m - 7)(3k + 2)$ 4. $5p^2(2q - p^2) + 3q(p - 2q)$