Question

using factor theorem x^3 +13x^2+ 32x +20​

Answer 1

$\bigstar\large \sf \underline \bold{ \underline{ \: SOLUTION}}\\ \\ \\</p><p></p><p>\bold\green{\underline{Let,}} \\ \\ \\ </p><p></p><p> \sf\bold{p(x ) = {x}^{3} + 13 {x}^{2} + 32x + 20} \\ \\ \\</p><p></p><p> \bf \underline{By \: trial, \: we \: find} \\ \\ \\</p><p> \sf\bold{p( - 1) = ( { - 1})^{3} + 13( - 1) {}^{2} + 32( - 1) + 20} \\ \\ \sf: \implies\bold{ - 1 + 13 - 32 + 20 = 0} \\ \\ \\</p><p></p><p>\bold{\fbox{\color{Red}{By\:factor\:theorem,}}} \pink\bigstar\\ \\ \\</p><p></p><p> \sf\bold{x-(-1) , (x+1) is \: a \: factor \: of \: p(x).} \\ \\ \\</p><p> \sf\bold{{x}^{3} + 13 {x}^{2} + 32 + 20} \\ \\ \\ \sf: \implies\bold{{x}^{2} (x + 1) + 12(x)( x + 1) + 20(x + 1) } \\ \\ \\ \sf: \implies\bold{(x + 1)( {x}^{2} + 12x + 20)} \\ \\ \\ \sf: \implies\bold{ (x + 1)( {x}^{2} + 2x + 10x + 20) } \\ \\ \\ \sf: \implies\bold{(x + 1){x(x + 2) + 10(x + 2)}} \\ \\ \\ \sf : \implies \bold { (x + 1)(x + 2)(x + 10)}$