Algebra I Factoring GCF \& Grouping Factor the following polynomials by GCF and/or groupin 1.) \( 5 x^{3}-6 x^{2}-5 x+6 \) 2.) \( 6 x^{3}+12 x^{2}+6 x \) 3.) \( x^{6}-x^{5}+x^{4}-x^{3} \) 4.) \( 10 x^{3}+15 x^{2}+20 x+30 \) 5.) \( 100 x^{7}-25 x^{5} \) 6.) \( 11 \mathrm{x}^{2}+44 x+33 \) 7.) \( 12 x^{5}-3 x^{3} \) 8.) \( -13 x^{15}-13 x^{12} \) 9.) \( 15 \mathrm{x}^{3}+2 x^{2}-x \) 10.) \( 16 x^{3}+56 x^{2}-18 x-63 \) 11.) \( 2 \mathrm{x}^{3}+3 x^{2}-18 x-27 \) 12.) \( -2 \mathrm{x}^{3}+54 \) 13.) \( 200 x^{2}-50 \) 14.) \( 24 x^{3}+4 x^{2}-54 x-9 \) 15.) \( 24 x^{3}-16 x^{2}-15 x+10 \)

Factor the expression by following steps: - step0: Factor: \(12x^{5}-3x^{3}\) - step1: Factor the expression: \(3x^{3}\left(4x^{2}-1\right)\) - step2: Factor the expression: \(3x^{3}\left(2x-1\right)\left(2x+1\right)\) Factor the expression \( 2 x^{3}+3 x^{2}-18 x-27 \). Factor the expression by following steps: - step0: Factor: \(2x^{3}+3x^{2}-18x-27\) - step1: Rewrite the expression: \(x^{2}\times 2x+x^{2}\times 3-9\times 2x-9\times 3\) - step2: Factor the expression: \(x^{2}\left(2x+3\right)-9\left(2x+3\right)\) - step3: Factor the expression: \(\left(x^{2}-9\right)\left(2x+3\right)\) - step4: Factor the expression: \(\left(x-3\right)\left(x+3\right)\left(2x+3\right)\) Factor the expression \( 24 x^{3}-16 x^{2}-15 x+10 \). Factor the expression by following steps: - step0: Factor: \(24x^{3}-16x^{2}-15x+10\) - step1: Calculate: \(24x^{3}-15x-16x^{2}+10\) - step2: Rewrite the expression: \(3x\times 8x^{2}-3x\times 5-2\times 8x^{2}+2\times 5\) - step3: Factor the expression: \(3x\left(8x^{2}-5\right)-2\left(8x^{2}-5\right)\) - step4: Factor the expression: \(\left(3x-2\right)\left(8x^{2}-5\right)\) Factor the expression \( 15 x^{3}+2 x^{2}-x \). Factor the expression by following steps: - step0: Factor: \(15x^{3}+2x^{2}-x\) - step1: Rewrite the expression: \(x\times 15x^{2}+x\times 2x-x\) - step2: Factor the expression: \(x\left(15x^{2}+2x-1\right)\) - step3: Factor the expression: \(x\left(3x+1\right)\left(5x-1\right)\) Factor the expression \( 200 x^{2}-50 \). Factor the expression by following steps: - step0: Factor: \(200x^{2}-50\) - step1: Factor the expression: \(50\left(4x^{2}-1\right)\) - step2: Factor the expression: \(50\left(2x-1\right)\left(2x+1\right)\) Factor the expression \( -13 x^{15}-13 x^{12 \). Factor the expression by following steps: - step0: Factor: \(-13x^{15}-13x^{12}\) - step1: Factor the expression: \(-13x^{12}\left(x^{3}+1\right)\) - step2: Factor the expression: \(-13x^{12}\left(x+1\right)\left(x^{2}-x+1\right)\) Factor the expression \( -2 x^{3}+54 \). Factor the expression by following steps: - step0: Factor: \(-2x^{3}+54\) - step1: Factor the expression: \(2\left(-x^{3}+27\right)\) - step2: Factor the expression: \(2\left(3-x\right)\left(9+3x+x^{2}\right)\) Factor the expression \( 24 x^{3}+4 x^{2}-54 x-9 \). Factor the expression by following steps: - step0: Factor: \(24x^{3}+4x^{2}-54x-9\) - step1: Rewrite the expression: \(4x^{2}\times 6x+4x^{2}-9\times 6x-9\) - step2: Factor the expression: \(4x^{2}\left(6x+1\right)-9\left(6x+1\right)\) - step3: Factor the expression: \(\left(4x^{2}-9\right)\left(6x+1\right)\) - step4: Factor the expression: \(\left(2x-3\right)\left(2x+3\right)\left(6x+1\right)\) Factor the expression \( 16 x^{3}+56 x^{2}-18 x-63 \). Factor the expression by following steps: - step0: Factor: \(16x^{3}+56x^{2}-18x-63\) - step1: Calculate: \(16x^{3}-18x+56x^{2}-63\) - step2: Rewrite the expression: \(2x\times 8x^{2}-2x\times 9+7\times 8x^{2}-7\times 9\) - step3: Factor the expression: \(2x\left(8x^{2}-9\right)+7\left(8x^{2}-9\right)\) - step4: Factor the expression: \(\left(2x+7\right)\left(8x^{2}-9\right)\) Factor the expression \( x^{6}-x^{5}+x^{4}-x^{3 \). Factor the expression by following steps: - step0: Factor: \(x^{6}-x^{5}+x^{4}-x^{3}\) - step1: Evaluate: \(x^{6}+x^{4}-x^{5}-x^{3}\) - step2: Rewrite the expression: \(x^{3}\times x^{3}+x^{3}\times x-x^{3}\times x^{2}-x^{3}\) - step3: Factor the expression: \(x^{3}\left(x^{3}+x-x^{2}-1\right)\) - step4: Factor the expression: \(x^{3}\left(x-1\right)\left(x^{2}+1\right)\) Factor the expression \( 6 x^{3}+12 x^{2}+6 x \). Factor the expression by following steps: - step0: Factor: \(6x^{3}+12x^{2}+6x\) - step1: Rewrite the expression: \(6x\times x^{2}+6x\times 2x+6x\) - step2: Factor the expression: \(6x\left(x^{2}+2x+1\right)\) - step3: Factor the expression: \(6x\left(x+1\right)^{2}\) Factor the expression \( 5 x^{3}-6 x^{2}-5 x+6 \). Factor the expression by following steps: - step0: Factor: \(5x^{3}-6x^{2}-5x+6\) - step1: Rewrite the expression: \(x^{2}\times 5x-x^{2}\times 6-5x+6\) - step2: Factor the expression: \(x^{2}\left(5x-6\right)-\left(5x-6\right)\) - step3: Factor the expression: \(\left(x^{2}-1\right)\left(5x-6\right)\) - step4: Factor the expression: \(\left(x-1\right)\left(x+1\right)\left(5x-6\right)\) Factor the expression \( 100 x^{7}-25 x^{5} \). Factor the expression by following steps: - step0: Factor: \(100x^{7}-25x^{5}\) - step1: Factor the expression: \(25x^{5}\left(4x^{2}-1\right)\) - step2: Factor the expression: \(25x^{5}\left(2x-1\right)\left(2x+1\right)\) Factor the expression \( 10 x^{3}+15 x^{2}+20 x+30 \). Factor the expression by following steps: - step0: Factor: \(10x^{3}+15x^{2}+20x+30\) - step1: Evaluate: \(10x^{3}+20x+15x^{2}+30\) - step2: Rewrite the expression: \(5\times 2x^{3}+5\times 4x+5\times 3x^{2}+5\times 6\) - step3: Factor the expression: \(5\left(2x^{3}+4x+3x^{2}+6\right)\) - step4: Factor the expression: \(5\left(2x+3\right)\left(x^{2}+2\right)\) Factor the expression \( 11 x^{2}+44 x+33 \). Factor the expression by following steps: - step0: Factor: \(11x^{2}+44x+33\) - step1: Rewrite the expression: \(11x^{2}+11\times 4x+11\times 3\) - step2: Factor the expression: \(11\left(x^{2}+4x+3\right)\) - step3: Factor the expression: \(11\left(x+1\right)\left(x+3\right)\) Here are the factored forms of the given polynomials using GCF and/or grouping: 1. **\( 5 x^{3}-6 x^{2}-5 x+6 \)** Factored form: \((x-1)(x+1)(5x-6)\) 2. **\( 6 x^{3}+12 x^{2}+6 x \)** Factored form: \(6x(x+1)^{2}\) 3. **\( x^{6}-x^{5}+x^{4}-x^{3} \)** Factored form: \(x^{3}(x-1)(x^{2}+1)\) 4. **\( 10 x^{3}+15 x^{2}+20 x+30 \)** Factored form: \(5(2x+3)(x^{2}+2)\) 5. **\( 100 x^{7}-25 x^{5} \)** Factored form: \(25x^{5}(4x^{2}-1)\) or \(25x^{5}(2x-1)(2x+1)\) 6. **\( 11 x^{2}+44 x+33 \)** Factored form: \(11(x+1)(x+3)\) 7. **\( 12 x^{5}-3 x^{3} \)** Factored form: \(3x^{3}(4x^{2}-1)\) or \(3x^{3}(2x-1)(2x+1)\) 8. **\( -13 x^{15}-13 x^{12} \)** Factored form: \(-13x^{12}(x+1)(x^{2}-x+1)\) 9. **\( 15 x^{3}+2 x^{2}-x \)** Factored form: \(x(3x+1)(5x-1)\) 10. **\( 16 x^{3}+56 x^{2}-18 x-63 \)** Factored form: \((2x+7)(8x^{2}-9)\) 11. **\( 2 x^{3}+3 x^{2}-18 x-27 \)** Factored form: \((x-3)(x+3)(2x+3)\) 12. **\( -2 x^{3}+54 \)** Factored form: \(2(3-x)(9+3x+x^{2})\) 13. **\( 200 x^{2}-50 \)** Factored form: \(50(2x-1)(2x+1)\) 14. **\( 24 x^{3}+4 x^{2}-54 x-9 \)** Factored form: \((2x-3)(2x+3)(6x+1)\) 15. **\( 24 x^{3}-16 x^{2}-15 x+10 \)** Factored form: \((3x-2)(8x^{2}-5)\) These factorizations utilize the greatest common factor (GCF) and grouping methods where applicable.