Question

Factor the polynomial 4n^3+20n^2-64n-320

Answer 1

$4n^3+20n^2-64n-320\\\\=\boxed{4n^2}\cdot n+\boxed{4n^2}\cdot5+\boxed{-64}\cdot n+\boxed{-64}\cdot5\\\\=\boxed{4n^2}(n+5)-\boxed{64}(n+5)\\\\=(n+5)(4n^2-64)\\\\=(n+5)(4\cdot n^2-4\cdot16)\\\\=(n+5)\cdot4(n^2-16)\\\\=4\cdot(n+5)(n^2-4^2)\ \ \ |use:a^2-b^2=(a-b)(a+b)\\\\\boxed{=4(n+5)(n-4)(n+4)}$