In Exercises \( 1-12 \), factor the polynomial. \( \begin{array}{lll}\text { 1. } 5 x^{2}-5 x-30 & \text { 2. } 8 x^{2}-16 x-192 & \text { 3. } 6 x^{2}+48 x+42 \\ \text { 4. } 12 j^{2}-32 j+5 & \text { 5. } 10 w^{2}+24 w+8 & \text { 6. } 3 y^{2}+y-14 \\ \text { 7. } 12 p^{2}-7 p-10 & \text { 8. } 15 d^{2}+16 d-15 & \text { 9. } 2 x^{2}+17 x-9 \\ \text { 10. }-9 v^{2}-22 v-8 & \text { 11. }-14 m^{2}+13 m-3 & \text { 12. }-20 q^{2}+56 q-15\end{array} \)

Factor the expression by following steps: - step0: Factor: \(-20q^{2}+56q-15\) - step1: Rewrite the expression: \(-20q^{2}+\left(6+50\right)q-15\) - step2: Calculate: \(-20q^{2}+6q+50q-15\) - step3: Rewrite the expression: \(-2q\times 10q+2q\times 3+5\times 10q-5\times 3\) - step4: Factor the expression: \(-2q\left(10q-3\right)+5\left(10q-3\right)\) - step5: Factor the expression: \(\left(-2q+5\right)\left(10q-3\right)\) - step6: Factor the expression: \(-\left(2q-5\right)\left(10q-3\right)\) Factor the expression \( 3y^{2}+y-14 \). Factor the expression by following steps: - step0: Factor: \(3y^{2}+y-14\) - step1: Rewrite the expression: \(3y^{2}+\left(7-6\right)y-14\) - step2: Calculate: \(3y^{2}+7y-6y-14\) - step3: Rewrite the expression: \(y\times 3y+y\times 7-2\times 3y-2\times 7\) - step4: Factor the expression: \(y\left(3y+7\right)-2\left(3y+7\right)\) - step5: Factor the expression: \(\left(y-2\right)\left(3y+7\right)\) Factor the expression \( 2x^{2}+17x-9 \). Factor the expression by following steps: - step0: Factor: \(2x^{2}+17x-9\) - step1: Rewrite the expression: \(2x^{2}+\left(-1+18\right)x-9\) - step2: Calculate: \(2x^{2}-x+18x-9\) - step3: Rewrite the expression: \(x\times 2x-x+9\times 2x-9\) - step4: Factor the expression: \(x\left(2x-1\right)+9\left(2x-1\right)\) - step5: Factor the expression: \(\left(x+9\right)\left(2x-1\right)\) Factor the expression \( 12p^{2}-7p-10 \). Factor the expression by following steps: - step0: Factor: \(12p^{2}-7p-10\) - step1: Rewrite the expression: \(12p^{2}+\left(-15+8\right)p-10\) - step2: Calculate: \(12p^{2}-15p+8p-10\) - step3: Rewrite the expression: \(3p\times 4p-3p\times 5+2\times 4p-2\times 5\) - step4: Factor the expression: \(3p\left(4p-5\right)+2\left(4p-5\right)\) - step5: Factor the expression: \(\left(3p+2\right)\left(4p-5\right)\) Factor the expression \( 6x^{2}+48x+42 \). Factor the expression by following steps: - step0: Factor: \(6x^{2}+48x+42\) - step1: Rewrite the expression: \(6x^{2}+6\times 8x+6\times 7\) - step2: Factor the expression: \(6\left(x^{2}+8x+7\right)\) - step3: Factor the expression: \(6\left(x+1\right)\left(x+7\right)\) Factor the expression \( 5x^{2}-5x-30 \). Factor the expression by following steps: - step0: Factor: \(5x^{2}-5x-30\) - step1: Rewrite the expression: \(5x^{2}-5x-5\times 6\) - step2: Factor the expression: \(5\left(x^{2}-x-6\right)\) - step3: Factor the expression: \(5\left(x-3\right)\left(x+2\right)\) Factor the expression \( 8x^{2}-16x-192 \). Factor the expression by following steps: - step0: Factor: \(8x^{2}-16x-192\) - step1: Rewrite the expression: \(8x^{2}-8\times 2x-8\times 24\) - step2: Factor the expression: \(8\left(x^{2}-2x-24\right)\) - step3: Factor the expression: \(8\left(x-6\right)\left(x+4\right)\) Factor the expression \( -9v^{2}-22v-8 \). Factor the expression by following steps: - step0: Factor: \(-9v^{2}-22v-8\) - step1: Factor the expression: \(-\left(9v^{2}+22v+8\right)\) - step2: Factor the expression: \(-\left(v+2\right)\left(9v+4\right)\) Factor the expression \( -14m^{2}+13m-3 \). Factor the expression by following steps: - step0: Factor: \(-14m^{2}+13m-3\) - step1: Rewrite the expression: \(-14m^{2}+\left(6+7\right)m-3\) - step2: Calculate: \(-14m^{2}+6m+7m-3\) - step3: Rewrite the expression: \(-2m\times 7m+2m\times 3+7m-3\) - step4: Factor the expression: \(-2m\left(7m-3\right)+7m-3\) - step5: Factor the expression: \(\left(-2m+1\right)\left(7m-3\right)\) - step6: Factor the expression: \(-\left(2m-1\right)\left(7m-3\right)\) Factor the expression \( 12j^{2}-32j+5 \). Factor the expression by following steps: - step0: Factor: \(12j^{2}-32j+5\) - step1: Rewrite the expression: \(12j^{2}+\left(-2-30\right)j+5\) - step2: Calculate: \(12j^{2}-2j-30j+5\) - step3: Rewrite the expression: \(2j\times 6j-2j-5\times 6j+5\) - step4: Factor the expression: \(2j\left(6j-1\right)-5\left(6j-1\right)\) - step5: Factor the expression: \(\left(2j-5\right)\left(6j-1\right)\) Factor the expression \( 15d^{2}+16d-15 \). Factor the expression by following steps: - step0: Factor: \(15d^{2}+16d-15\) - step1: Rewrite the expression: \(15d^{2}+\left(-9+25\right)d-15\) - step2: Calculate: \(15d^{2}-9d+25d-15\) - step3: Rewrite the expression: \(3d\times 5d-3d\times 3+5\times 5d-5\times 3\) - step4: Factor the expression: \(3d\left(5d-3\right)+5\left(5d-3\right)\) - step5: Factor the expression: \(\left(3d+5\right)\left(5d-3\right)\) Factor the expression \( 10w^{2}+24w+8 \). Factor the expression by following steps: - step0: Factor: \(10w^{2}+24w+8\) - step1: Rewrite the expression: \(2\times 5w^{2}+2\times 12w+2\times 4\) - step2: Factor the expression: \(2\left(5w^{2}+12w+4\right)\) - step3: Factor the expression: \(2\left(w+2\right)\left(5w+2\right)\) Here are the factored forms of the given polynomials: 1. \( 5x^{2}-5x-30 = 5(x-3)(x+2) \) 2. \( 8x^{2}-16x-192 = 8(x-6)(x+4) \) 3. \( 6x^{2}+48x+42 = 6(x+1)(x+7) \) 4. \( 12j^{2}-32j+5 = (2j-5)(6j-1) \) 5. \( 10w^{2}+24w+8 = 2(w+2)(5w+2) \) 6. \( 3y^{2}+y-14 = (y-2)(3y+7) \) 7. \( 12p^{2}-7p-10 = (3p+2)(4p-5) \) 8. \( 15d^{2}+16d-15 = (3d+5)(5d-3) \) 9. \( 2x^{2}+17x-9 = (x+9)(2x-1) \) 10. \( -9v^{2}-22v-8 = -(v+2)(9v+4) \) 11. \( -14m^{2}+13m-3 = -(2m-1)(7m-3) \) 12. \( -20q^{2}+56q-15 = -(2q-5)(10q-3) \) If you need further assistance or explanations on any specific polynomial, feel free to ask!