factor x^3+2x^2-36x-72

{ "query": { "display": "factor $$x^{3}+2x^{2}-36x-72$$", "symbolab_question": "FACTOR#factor x^{3}+2x^{2}-36x-72" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "(x+2)(x+6)(x-6)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Factor $$x^{3}+2x^{2}-36x-72:{\\quad}\\left(x+2\\right)\\left(x+6\\right)\\left(x-6\\right)$$", "input": "x^{3}+2x^{2}-36x-72", "steps": [ { "type": "step", "result": "=\\left(x^{3}+2x^{2}\\right)+\\left(-36x-72\\right)" }, { "type": "interim", "title": "Factor out $$x^{2}\\:$$from $$x^{3}+2x^{2}:\\quad\\:x^{2}\\left(x+2\\right)$$", "input": "x^{3}+2x^{2}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$a^{b+c}=a^{b}a^{c}$$", "secondary": [ "$$x^{3}=xx^{2}$$" ], "result": "=xx^{2}+2x^{2}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "Factor out common term $$x^{2}$$", "result": "=x^{2}\\left(x+2\\right)", "meta": { "practiceLink": "/practice/factoring-practice", "practiceTopic": "Factoring" } } ], "meta": { "interimType": "Factor Out Specific 3Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s73Ef68PtVnVVO8oet6Rl52TP9tq0GAd+koc1SS3zfPPEH9A8JFyuzjx7kca+eJh9pxjKoMzc0d1qWN5qd2LftJoYralHdxr30XPVyZ0Ce5xrwt9LEn7QCBUukJKctfSJKBKLYW6gy9hK+Dkh1Oj9+2SI5uPGed86ldUJFp22f5aJ1HRtqt5/2sCXmoGEqNRf7sIjaxJ4DvjTb2fbKjbvtlQ==" } }, { "type": "interim", "title": "Factor out $$-36\\:$$from $$-36x-72:\\quad\\:-36\\left(x+2\\right)$$", "input": "-36x-72", "steps": [ { "type": "step", "primary": "Rewrite $$-72$$ as $$-36\\cdot\\:2$$", "result": "=-36x-36\\cdot\\:2" }, { "type": "step", "primary": "Factor out common term $$-36$$", "result": "=-36\\left(x+2\\right)", "meta": { "practiceLink": "/practice/factoring-practice", "practiceTopic": "Factoring" } } ], "meta": { "interimType": "Factor Out Specific 3Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7BuAhz2fjmqlhwZZWkIBjKe6WhAHlhVR5DrUCfvc0BZjFeNKI8a2kiIgBIHIyg9qrxnSLtydOn+P6AMBdN/vP25eRymX25MRVDlGApUYaecqF4aOVLaBuuVKS9lqM99wwqrSIOMakpcB5odRMNLcIh8IhXnQhwQ8SfAPFxIOJ4rb+iJS+guaOeWn3nQIq727R" } }, { "type": "step", "result": "=x^{2}\\left(x+2\\right)-36\\left(x+2\\right)" }, { "type": "step", "primary": "Factor out common term $$x+2$$", "result": "=\\left(x+2\\right)\\left(x^{2}-36\\right)", "meta": { "practiceLink": "/practice/factoring-practice", "practiceTopic": "Factoring" } }, { "type": "interim", "title": "Factor $$x^{2}-36:{\\quad}\\left(x+6\\right)\\left(x-6\\right)$$", "input": "x^{2}-36", "steps": [ { "type": "step", "primary": "Rewrite $$36$$ as $$6^{2}$$", "result": "=x^{2}-6^{2}" }, { "type": "step", "primary": "Apply Difference of Two Squares Formula: $$x^{2}-y^{2}=\\left(x+y\\right)\\left(x-y\\right)$$", "secondary": [ "$$x^{2}-6^{2}=\\left(x+6\\right)\\left(x-6\\right)$$" ], "result": "=\\left(x+6\\right)\\left(x-6\\right)", "meta": { "practiceLink": "/practice/factoring-practice#area=main&subtopic=Difference%20of%20Two%20Squares", "practiceTopic": "Factor Difference of Squares" } } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Factor Specific 1Eq" } }, { "type": "step", "result": "=\\left(x+2\\right)\\left(x+6\\right)\\left(x-6\\right)" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }