{"type":"video","version":"1.0","html":"<iframe src=\"https://www.loom.com/embed/0bde2c15e1ce4df1af41993fe1ba2d05\" frameborder=\"0\" width=\"1920\" height=\"1440\" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>","height":1440,"width":1920,"provider_name":"Loom","provider_url":"https://www.loom.com","thumbnail_height":1440,"thumbnail_width":1920,"thumbnail_url":"https://cdn.loom.com/sessions/thumbnails/0bde2c15e1ce4df1af41993fe1ba2d05-b07692ec3a9ea58a.gif","duration":2054.933,"title":"8MA0 Pure 10 Proof","description":"In this video, I walk through several mathematical proofs and concepts, including the divisibility of expressions and the nature of roots in quadratic equations. I demonstrate that for all positive integers, certain expressions are divisible by 6 and prove that n cubed plus 2 is not divisible by 8. Additionally, I explore the conditions under which quadratic equations have no real roots and show that specific expressions are always greater than zero. I encourage viewers to engage with the material by considering counterexamples and applying the concepts discussed. Please review the proofs and examples provided to solidify your understanding of these mathematical principles."}