Question

$by ferrari \: method \: 9 {x}^{4} + 12 {x}^{3} + 9 {x }^{2} - 2x - 8 = 0$
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Answer 1

$question \\ = 9 {x}^{4} + 12 {x}^{3} + 9 {x }^{2} - 2x - 8 = 0 \\ solution. \\ let. \: \: p(x)\: = \: x + 1 = 0 \\p(x) = x = - 1 \\ p( - 1) \\ on \: keeping \: in \: polynomial \\ p(x) = 9 {x}^{4} + 12 {x}^{3} + 9 {x }^{2} - 2x - 8 = 0 \\ p( - 1) = 9( { - 1}^{4}) + 12( { - 1}^{3}) + 9( { - 1}^{2}) \\ - 2( - 1) - 8 = 0 \\ = 9(1) + 12( - 1) + 9(1) + 2 - 8 = 0 \\ 9 - 12 + 9 + 2 - 8 = 0 \\ 9 - 12 + 11 - 8 = 0 \\ 9 + 11 - 12 - 8 = 0 \\ 20 - 20 = 0 \\ 0 = 0 \\ l.h.s = r.h.s \\ proved...$