factor-21n^5-14n^4+7n^2

{ "query": { "display": "factor $$-21n^{5}-14n^{4}+7n^{2}$$", "symbolab_question": "FACTOR#factor -21n^{5}-14n^{4}+7n^{2}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "7n^{2}(-3n^{3}-2n^{2}+1)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Factor $$-21n^{5}-14n^{4}+7n^{2}:{\\quad}7n^{2}\\left(-3n^{3}-2n^{2}+1\\right)$$", "input": "-21n^{5}-14n^{4}+7n^{2}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$a^{b+c}=a^{b}a^{c}$$", "secondary": [ "$$n^{4}=n^{2}n^{2}$$", "$$n^{5}=n^{3}n^{2}$$" ], "result": "=-21n^{3}n^{2}-14n^{2}n^{2}+7n^{2}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "Rewrite $$21$$ as $$7\\cdot\\:3$$", "secondary": [ "Rewrite $$14$$ as $$7\\cdot\\:2$$", "Rewrite $$7$$ as $$7\\cdot\\:1$$" ], "result": "=-7\\cdot\\:3n^{3}n^{2}-7\\cdot\\:2n^{2}n^{2}+7\\cdot\\:1\\cdot\\:n^{2}" }, { "type": "step", "primary": "Factor out common term $$7n^{2}$$", "result": "=7n^{2}\\left(-3n^{3}-2n^{2}+1\\right)", "meta": { "practiceLink": "/practice/factoring-practice", "practiceTopic": "Factoring" } } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }